ParityCheck -- an optional input for the linearCode constructor

Description

This is a Boolean symbol, returns value false or true. The default value is false.

This symbol is provided by the package CodingTheory.

i1 : F = GF(4,Variable => a);

i2 : L = {{1,0,a,0,0},{0,a,a+1,1,0},{1,1,1,a,0}};

i3 : M = matrix L;

             3      5
o3 : Matrix F  <-- F

i4 : C = linearCode(F,L,ParityCheck => true);

i5 : C.GeneratorMatrix;

             2      5
o5 : Matrix F  <-- F

i6 : C.ParityCheckMatrix

o6 = | 1 0 a   0 0 |
     | 0 a a+1 1 0 |
     | 1 1 1   a 0 |

             3      5
o6 : Matrix F  <-- F

generatorToParityCheck -- parity check matrix of a linear code
ParityCheckMatrix -- a parity check matrix of a code
ParityCheckRows -- rows of a parity check matrix of a code
parityCheckToGenerator -- generator matrix given a parity check matrix
randLDPC -- low density parity check matrix
tannerGraph -- outputs the tanner graph associated with the given parity check matrix

linearCode(...,ParityCheck=>...) -- see linearCode -- functions to construct linear codes over Galois fields

The object ParityCheck is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CodingTheory.m2:3003:0.