The operations described here produce a new code by modifying in some way the codewords of a given code.
Construct a new additive code by including the all-ones vector with the words of the additive code C.
Given a subcode S of the code C, return a code C' such that C=S + C'. Both C and S must be defined over the same field.
Given codes C and D, form the code that is direct sum of C and D. The direct sum consists of all vectors u|v, where u ∈C and v ∈D.
Given a sequence of codes Q = [C1, ..., Cr], all defined over the same field F, construct the direct sum of the Ci.
Given an [n1, k1] code C and an [n2, k2] code D, both over the same ring R, construct the direct product of C and D. The direct product has length n1.n2 and its generator matrix is the Kronecker product of the basis matrices of C and D.
Given an [n, k, d] additive 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.
Return the code obtained by extending the code C extended n times.
Add n zeros to the end of each codeword of the code C.
Given codes C1 and C2 defined over the same alphabet, return the code consisting of all vectors of the form u|u + v, where u ∈C1 and v ∈C2. Zeros are appended where needed to make up any length differences in the two codes.
a: FldFinElt Default: -1
Given three codes C1, C2 and C3 defined over the same alphabet K, return the code consisting of all vectors of the form u|u + a * v|u + v + w, where u ∈C1, v ∈C2 and w ∈C3. The default value of the multiplier a is a primitive element of K. Zeros are appended where needed to ensure that every codeword has the same length.
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.
Given an [n, k] code C and a set S of distinct integers { i1, ..., ir } each of which lies in the range [1, n], construct a new code C' by deleting the components i1, ..., ir 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.
Given an [n, k] code C and a set S of distinct integers { i1, ..., ir}, 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 i1, ..., ir, and deleting these components. Thus, the resulting code will have length n - r.
Given codes C1 and C2, both defined over the same field K, return the concatenation C of C1 and C2. The generators of the resultant code are the concatenations of the generators of C1 and C2.
Given an [n1, k, d1] code C1 and an [n2, k, d2] code C2 of the same dimension, where both codes are defined over the same field K, this function returns a [n1 + n2, k, ≥d1 + d2] code whose generator matrix is HorizontalJoin(A, B), where A and B are the generator matrices for codes C1 and C2, respectively.