65.62 ReedMullerCode

ReedMullerCode( r, k )

ReedMullerCode returns a binary Reed-Muller code R(<r>, <k>) with dimension k and order r. This is a code with length 2^<k> and minimum distance 2^{<k>-<r>}. By definition, the <r>^{th} order binary Reed-Muller code of length n=2^<m>, for 0 leq <r> leq <m>, is the set of all vectors f, where f is a Boolean function which is a polynomial of degree at most r.

    gap> ReedMullerCode( 1, 3 );
    a linear [8,4,4]2 Reed-Muller (1,3) code over GF(2)