The operations described here produce a new code by modifying in some way, the code words of a given code.

AugmentCode(C) : Code -> Code

Given an [n, k] binary code C, construct a new code C' by including the all-ones vector with the words of C (provided that it is not already in C).

Given an [n_1, k_1] code C and an [n_2, k_2] code D, both over the same field K, construct the direct sum of C and D. The direct sum consists of all vectors u|v, where u in C and v in D.

Given an [n, k, d] code C form a new code C' from C by adding the appropriate extra coordinate to each vector of C such that the sum of the coordinates of the extended vector is zero. (Thus if C is a binary code, the construction will add a 0 at the end of every codeword having even weight, and a 1 at the end of every codeword having odd weight.)

Given an [n, k] binary code containing codewords of both even and odd weight, construct a new code C' by deleting all the code words of C having odd weight.

Given an [n, k] binary code C, construct a new code by first adding the all-ones codeword, and then extending it by adding an overall parity check.

Given an [n, k_1] code C and an [n, k_2] code D, both over the same field K, construct the direct sum of C and D. The Plotkin sum consists of all vectors u|u + v, where the vertical bar denotes concatenation of vectors.

Given an [n, k] code C, and an integer i, 1 <= i <= n, construct a new code C' by deleting the i-th coordinate from each code word of C.

PunctureCode(C, S) : Code, { RngIntElt } -> Code

Given an [n, k] code C and a set S of distinct integers { i_1, ..., i_r } each of which lies in the range [1, n], construct a new code C' by deleting the components i_1, ..., i_r from each code word of C.

Given an [n, k] code C and an integer i, 1 <= i <= n, construct a new code from C by selecting only those codewords of C having a zero as their i-th component and deleting the i-th component from these codewords. Thus, the resulting code will have length n - 1.

ShortenCode(C, S) : Code, { RngIntElt } -> Code

Given an [n, k] code C and a set S of distinct integers { i_1, ..., i_r} each of which lies in the range [1, n], construct a new code from C by selecting only those codewords of C having zeros in each of the coordinate positions i_1, ..., i_r, and deleting these components. Thus, the resulting code will have length n - r.