linearCode(G)
linearCode(M)
linearCode(M,L)
linearCode(F,L)
linearCode(F,n,L)
linearCode(p,r,n,L)
We present below the ways in how a linear code $C$ can be defined.
linearCode(G)
Given a matrix G, whose entries are in a Galois field F, this function returns a linear code $C$ over F.
If no optional input is specified, then the generator matrix of the code $C$ is G.
If the optional input ParityCheck => true is specified, then the code $C$ is the dual of the linear code generated by the matrix G.
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This is an example using the optional argument ParityCheck=>true.
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linearCode(M)
Given a submodule M of a free module F$^n$, where $F$ is a Galois field, this function returns a linear code $C$ whose ambient space is F$^n$.
If no optional input is specified, then the code $C$ is generated by the elements of M.
If the optional input ParityCheck => true is specified, then the code $C$ is the dual of the linear code generated by the elements of M.
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linearCode(M,L)
Given a free module M$=F^n$, where $F$ is a Galois field, and a non-empty list L of vectors of M, this function returns a linear code $C$ whose ambient space is $F^n$.
If no optional input is specified, then the code $C$ is generated by the vectors of L.
If the optional input ParityCheck => true is specified, then the code $C$ is the dual of the linear code generated by the vectors of L.
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This is an example using the optional argument ParityCheck=>true.
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linearCode(F,L)
Given a Galois field F, and a non-empty list L of vectors of the same size and whose entries are coercible into the field F, this function returns a linear code $C$ over the field F.
If no optional input is specified, then the code $C$ is generated by the vectors of L.
If the optional input ParityCheck => true is specified, then the code $C$ is the dual of the linear code generated by the vectors of L.
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This is an example using the optional argument ParityCheck=>true.
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linearCode(F,n,L)
Given a Galois field F, a positive integer n, and a non-empty list L of vectors of size n and entries that are coercible into the field F, this function returns a linear code $C$ of length n over the field F.
If no optional input is specified, then the code $C$ is generated by the vectors of L.
If the optional input ParityCheck => true is specified, then the code $C$ is the dual of the linear code generated by the vectors of L.
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This is an example using the optional argument ParityCheck=>true.
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linearCode(p,r,n,L)
Given a prime number p, positive integers r and n, and a non-empty list L of vectors of size n and entries that are coercible into the Galois field GF$(\mathtt{p}^\mathtt{r})$, this function returns a linear code $C$ of length n over the Galois field GF$(\mathtt{p}^\mathtt{r})$.
If no optional input is specified, then the code $C$ is generated by the vectors of L.
If the optional input ParityCheck => true is specified, then the code $C$ is the dual of the linear code generated by the vectors of L.
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While some functions may work even when a ring is given, instead of a finite field, it is possible that the results are not the expected ones.
The object linearCode is a method function with options.