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67  <div class="navpath"><b>itpp</b>::<a class="el" href="classitpp_1_1GF.html">GF</a>
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71<h1>itpp::GF Class Reference</h1><!-- doxytag: class="itpp::GF" -->Galois Field GF(q). 
72<a href="#_details">More...</a>
73<p>
74<code>#include &lt;<a class="el" href="galois_8h-source.html">galois.h</a>&gt;</code>
75<p>
76
77<p>
78<a href="classitpp_1_1GF-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
79<tr><td></td></tr>
80<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
81<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0436dff6aebfa5093654a31e0bc6438a"></a><!-- doxytag: member="itpp::GF::GF" ref="0436dff6aebfa5093654a31e0bc6438a" args="()" -->
82&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#0436dff6aebfa5093654a31e0bc6438a">GF</a> ()</td></tr>
83
84<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor. <br></td></tr>
85<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b024dbc1cb60922bb00aecce96d471ed"></a><!-- doxytag: member="itpp::GF::GF" ref="b024dbc1cb60922bb00aecce96d471ed" args="(int qvalue)" -->
86&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#b024dbc1cb60922bb00aecce96d471ed">GF</a> (int qvalue)</td></tr>
87
88<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor. <br></td></tr>
89<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="009217ddab835ae84ee843fc328747a7"></a><!-- doxytag: member="itpp::GF::GF" ref="009217ddab835ae84ee843fc328747a7" args="(int qvalue, int inexp)" -->
90&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#009217ddab835ae84ee843fc328747a7">GF</a> (int qvalue, int inexp)</td></tr>
91
92<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor. <br></td></tr>
93<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="babae7d9d1b114864d4b00322871512b"></a><!-- doxytag: member="itpp::GF::GF" ref="babae7d9d1b114864d4b00322871512b" args="(const GF &amp;ingf)" -->
94&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#babae7d9d1b114864d4b00322871512b">GF</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
95
96<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Copy constructor. <br></td></tr>
97<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="998f0a59e3bcc6274bd9a7974efa331a"></a><!-- doxytag: member="itpp::GF::set" ref="998f0a59e3bcc6274bd9a7974efa331a" args="(int qvalue, int inexp)" -->
98void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#998f0a59e3bcc6274bd9a7974efa331a">set</a> (int qvalue, int inexp)</td></tr>
99
100<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">GF(q) equals <em>alpha</em> ^ <em>inexp</em>. <br></td></tr>
101<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#5e2187d93e23ec314f5932eb367be2a0">set</a> (int qvalue, const bvec &amp;vectorspace)</td></tr>
102
103<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">GF(q) equals the element that corresponds to the given vector space.  <a href="#5e2187d93e23ec314f5932eb367be2a0"></a><br></td></tr>
104<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="92df68dd5d84663cf20c21d1486aed48"></a><!-- doxytag: member="itpp::GF::set_size" ref="92df68dd5d84663cf20c21d1486aed48" args="(int qvalue)" -->
105void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#92df68dd5d84663cf20c21d1486aed48">set_size</a> (int qvalue)</td></tr>
106
107<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">set q=2^mvalue <br></td></tr>
108<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3202541d083d2927dd8ab3f07b18fb59"></a><!-- doxytag: member="itpp::GF::get_size" ref="3202541d083d2927dd8ab3f07b18fb59" args="() const " -->
109int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#3202541d083d2927dd8ab3f07b18fb59">get_size</a> () const </td></tr>
110
111<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return q. <br></td></tr>
112<tr><td class="memItemLeft" nowrap align="right" valign="top">bvec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#f9264d13f184870d06cb25aaf6c105b9">get_vectorspace</a> () const </td></tr>
113
114<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns the vector space representation of GF(q).  <a href="#f9264d13f184870d06cb25aaf6c105b9"></a><br></td></tr>
115<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87beac57ebd7f597cd409b04af9d5920"></a><!-- doxytag: member="itpp::GF::get_value" ref="87beac57ebd7f597cd409b04af9d5920" args="() const " -->
116int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#87beac57ebd7f597cd409b04af9d5920">get_value</a> () const </td></tr>
117
118<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns the alpha exponent. <br></td></tr>
119<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5a5ee69ed611dd6cada367cc241258f1"></a><!-- doxytag: member="itpp::GF::operator==" ref="5a5ee69ed611dd6cada367cc241258f1" args="(const GF &amp;ingf) const " -->
120int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#5a5ee69ed611dd6cada367cc241258f1">operator==</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf) const </td></tr>
121
122<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Equality check. <br></td></tr>
123<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="126d10787539dff093bbc04a2456ecca"></a><!-- doxytag: member="itpp::GF::operator!=" ref="126d10787539dff093bbc04a2456ecca" args="(const GF &amp;ingf) const " -->
124int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#126d10787539dff093bbc04a2456ecca">operator!=</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf) const </td></tr>
125
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Not-equality check. <br></td></tr>
127<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6baaf62e11dd55e38a5917eaccda8002"></a><!-- doxytag: member="itpp::GF::operator=" ref="6baaf62e11dd55e38a5917eaccda8002" args="(const GF &amp;ingf)" -->
128void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#6baaf62e11dd55e38a5917eaccda8002">operator=</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
129
130<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">GF(q) equals ingf. <br></td></tr>
131<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8de4f28df9388592904f9cafc3ed13ed"></a><!-- doxytag: member="itpp::GF::operator=" ref="8de4f28df9388592904f9cafc3ed13ed" args="(const int inexp)" -->
132void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#8de4f28df9388592904f9cafc3ed13ed">operator=</a> (const int inexp)</td></tr>
133
134<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">GF(q) equals alpha^inexp. <br></td></tr>
135<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e52540b90d82cc61f87ab440793919ad"></a><!-- doxytag: member="itpp::GF::operator+=" ref="e52540b90d82cc61f87ab440793919ad" args="(const GF &amp;ingf)" -->
136void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#e52540b90d82cc61f87ab440793919ad">operator+=</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
137
138<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">sum of two GF(q) <br></td></tr>
139<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="57c153da205a2b8362f03cbeaac7d2f5"></a><!-- doxytag: member="itpp::GF::operator+" ref="57c153da205a2b8362f03cbeaac7d2f5" args="(const GF &amp;ingf) const " -->
140<a class="el" href="classitpp_1_1GF.html">GF</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#57c153da205a2b8362f03cbeaac7d2f5">operator+</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf) const </td></tr>
141
142<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">sum of two GF(q) <br></td></tr>
143<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="77fd7d835894198e7f1d4e6f2df72545"></a><!-- doxytag: member="itpp::GF::operator&#45;=" ref="77fd7d835894198e7f1d4e6f2df72545" args="(const GF &amp;ingf)" -->
144void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#77fd7d835894198e7f1d4e6f2df72545">operator-=</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
145
146<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Difference of two GF(q), same as sum for q=2^m. <br></td></tr>
147<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2d8c65c93ecd2e0fb66ec2db0e48d34c"></a><!-- doxytag: member="itpp::GF::operator&#45;" ref="2d8c65c93ecd2e0fb66ec2db0e48d34c" args="(const GF &amp;ingf) const " -->
148<a class="el" href="classitpp_1_1GF.html">GF</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#2d8c65c93ecd2e0fb66ec2db0e48d34c">operator-</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf) const </td></tr>
149
150<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Difference of two GF(q), same as sum for q=2^m. <br></td></tr>
151<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="92e4e4a8aef619814741f771d1e4fdfc"></a><!-- doxytag: member="itpp::GF::operator*=" ref="92e4e4a8aef619814741f771d1e4fdfc" args="(const GF &amp;ingf)" -->
152void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#92e4e4a8aef619814741f771d1e4fdfc">operator*=</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
153
154<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">product of two GF(q) <br></td></tr>
155<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e6b155ed86bc5eb7bf5593a11fb41483"></a><!-- doxytag: member="itpp::GF::operator*" ref="e6b155ed86bc5eb7bf5593a11fb41483" args="(const GF &amp;ingf) const " -->
156<a class="el" href="classitpp_1_1GF.html">GF</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#e6b155ed86bc5eb7bf5593a11fb41483">operator*</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf) const </td></tr>
157
158<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">product of two GF(q) <br></td></tr>
159<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b789a0bc8f1bd4130b87d01500c1606f"></a><!-- doxytag: member="itpp::GF::operator/=" ref="b789a0bc8f1bd4130b87d01500c1606f" args="(const GF &amp;ingf)" -->
160void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#b789a0bc8f1bd4130b87d01500c1606f">operator/=</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
161
162<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">division of two GF(q) <br></td></tr>
163<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="15d6722131ec097cc5051ab9ba3590cc"></a><!-- doxytag: member="itpp::GF::operator/" ref="15d6722131ec097cc5051ab9ba3590cc" args="(const GF &amp;ingf) const " -->
164<a class="el" href="classitpp_1_1GF.html">GF</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#15d6722131ec097cc5051ab9ba3590cc">operator/</a> (const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf) const </td></tr>
165
166<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">product of two GF(q) <br></td></tr>
167<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
168<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="80fbd553165f964a5c4ffcf3c30c9388"></a><!-- doxytag: member="itpp::GF::operator&lt;&lt;" ref="80fbd553165f964a5c4ffcf3c30c9388" args="(std::ostream &amp;os, const GF &amp;ingf)" -->
169std::ostream &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1GF.html#80fbd553165f964a5c4ffcf3c30c9388">operator&lt;&lt;</a> (std::ostream &amp;os, const <a class="el" href="classitpp_1_1GF.html">GF</a> &amp;ingf)</td></tr>
170
171<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Output stream for GF(q). <br></td></tr>
172</table>
173<hr><a name="_details"></a><h2>Detailed Description</h2>
174Galois Field GF(q).
175<p>
176<dl class="author" compact><dt><b>Author:</b></dt><dd>Tony Ottosson</dd></dl>
177Galois field GF(q), where <em>q</em> = 2^m. Possible <em>m</em> values is <em>m</em> = 1,2,...,16. Elements are given as exponents of the primitive element <em>alpha</em>. Observe that the zeroth element are given as "-1". ( log(0)=-Inf ). <h3>The following primitve polynomials are used to construct the fields:</h3>
178<p>
179<ul>
180<li>
181GF(4): 1+x+x^2  </li>
182<li>
183GF(8): 1+x+x^3  </li>
184<li>
185GF(16): 1+x+x^4  </li>
186<li>
187GF(32): 1+x^2+x^5  </li>
188<li>
189GF(64): 1+x^2+x^6  </li>
190<li>
191GF(128): 1+x^3+x^7  </li>
192<li>
193GF(256): 1+x^2+x^3+x^4+x^8  </li>
194<li>
195GF(512): 1+x^4+x^9  </li>
196<li>
197GF(1024): 1+x^3+x^10  </li>
198<li>
199<a class="el" href="classitpp_1_1GF.html" title="Galois Field GF(q).">GF</a>(2^11): 1+x^2+x^11  </li>
200<li>
201<a class="el" href="classitpp_1_1GF.html" title="Galois Field GF(q).">GF</a>(2^12): 1+x+x^4+x^12  </li>
202<li>
203<a class="el" href="classitpp_1_1GF.html" title="Galois Field GF(q).">GF</a>(2^13): 1+x+x^3+x^4+x^13  </li>
204<li>
205<a class="el" href="classitpp_1_1GF.html" title="Galois Field GF(q).">GF</a>(2^14): 1+x+x^3+x^5+x^14  </li>
206<li>
207<a class="el" href="classitpp_1_1GF.html" title="Galois Field GF(q).">GF</a>(2^15): 1+x+x^15  </li>
208<li>
209<a class="el" href="classitpp_1_1GF.html" title="Galois Field GF(q).">GF</a>(2^16): 1+x+x^3+x^12+x^16  </li>
210</ul>
211<p>
212As indicated it is possible to use this class for binary elements, that is GF(2). However, this is less efficient in storage (each element take 5 bytes of memory) and in speed. If possible use the class BIN instead. Observe, also that the element "0" is called "-1" and "1" called "0". <hr><h2>Member Function Documentation</h2>
213<a class="anchor" name="f9264d13f184870d06cb25aaf6c105b9"></a><!-- doxytag: member="itpp::GF::get_vectorspace" ref="f9264d13f184870d06cb25aaf6c105b9" args="() const " -->
214<div class="memitem">
215<div class="memproto">
216      <table class="memname">
217        <tr>
218          <td class="memname">bvec itpp::GF::get_vectorspace           </td>
219          <td>(</td>
220          <td class="paramname">          </td>
221          <td>&nbsp;)&nbsp;</td>
222          <td> const<code> [inline]</code></td>
223        </tr>
224      </table>
225</div>
226<div class="memdoc">
227
228<p>
229Returns the vector space representation of GF(q).
230<p>
231The format is (...,c,b,a), where the element x is given as x=...+c*alpha^2+b*alpha+a.
232<p>References <a class="el" href="group__convertfunc.html#g83db366182e10eb823bcd5cb0149adf3">itpp::dec2bin()</a>.</p>
233
234</div>
235</div><p>
236<a class="anchor" name="5e2187d93e23ec314f5932eb367be2a0"></a><!-- doxytag: member="itpp::GF::set" ref="5e2187d93e23ec314f5932eb367be2a0" args="(int qvalue, const bvec &amp;vectorspace)" -->
237<div class="memitem">
238<div class="memproto">
239      <table class="memname">
240        <tr>
241          <td class="memname">void itpp::GF::set           </td>
242          <td>(</td>
243          <td class="paramtype">int&nbsp;</td>
244          <td class="paramname"> <em>qvalue</em>, </td>
245        </tr>
246        <tr>
247          <td class="paramkey"></td>
248          <td></td>
249          <td class="paramtype">const bvec &amp;&nbsp;</td>
250          <td class="paramname"> <em>vectorspace</em></td><td>&nbsp;</td>
251        </tr>
252        <tr>
253          <td></td>
254          <td>)</td>
255          <td></td><td></td><td><code> [inline]</code></td>
256        </tr>
257      </table>
258</div>
259<div class="memdoc">
260
261<p>
262GF(q) equals the element that corresponds to the given vector space.
263<p>
264The format is (...,c,b,a), where the element x is given as x=...+c*alpha^2+b*alpha+a.
265<p>References <a class="el" href="group__convertfunc.html#g698adf78bc0f9d36fd5987bc87d543fa">itpp::bin2dec()</a>, <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="galois_8cpp-source.html#l00042">set_size()</a>.</p>
266
267</div>
268</div><p>
269<hr>The documentation for this class was generated from the following files:<ul>
270<li><a class="el" href="galois_8h-source.html">galois.h</a><li><a class="el" href="galois_8cpp.html">galois.cpp</a></ul>
271</div>
272<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:19 2009 for mixpp by&nbsp;
273<a href="http://www.doxygen.org/index.html">
274<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
275</body>
276</html>
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