65.65 AlternantCode

AlternantCode( r, Y, F )
AlternantCode( r, Y, alpha, F )

AlternantCode returns an alternant code, with parameters r, Y and alpha (optional). r is the design redundancy of the code. Y and alpha are both vectors of length n from which the parity check matrix is constructed. The check matrix has entries of the form a_i^j y_i. If no alpha is specified, the vector [1, a, a^2, .., a^{n-1}] is used, where a is a primitive element of a Galois field F.

    gap> Y := [ 1, 1, 1, 1, 1, 1, 1];; a := PrimitiveUnityRoot( 2, 7 );;
    gap> alpha := List( [0..6], i -> a^i );;
    gap> C := AlternantCode( 2, Y, alpha, GF(8) );
    a linear [7,3,3..4]3..4 alternant code over GF(8) 

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