Given an [n, k, d] code C defined over the field K, and an extension field L of K, construct the code C' over L corresponding to C. The function also returns the embeddding map from C into C'.

Given an [n, k, d] code C defined over the field K, and a subfield S of K such that the degree of K over S is m, construct a new [N = mn, k, D >= d] code C' over S by replacing each component of each codeword of C by its representation as a vector over S. The function also returns the isomorphism from C onto C'.

RestrictField(C, S) : Code, FldFin -> Code, Map

SubfieldSubcode(C) : Code -> Code, Map

RestrictField(C) : Code -> Code, Map

Given an [n, k, d] code C defined over the field K, and a subfield S of K, construct a new [n, K <= k, D >= d] code C' over S consisting of the codewords of C which have all their components in S. If S is omitted, it is taken to be the prime subfield of K. The function also returns the restriction map from C to the subfield subcode C'.

Trace(C) : Code -> Code

Given a code C defined over the field K, and a subfield S of K, construct a new code C' over S consisting of the traces with respect to S of each of the codewords of C. If S is omitted, it is taken to be the prime subfield of K.