Additive Codes over Finite Fields [HB 116]

A new package for additive codes has been included in this release. Given a finite field F and the space of all n-tuples of F, an additive code is a subset of F⁽ⁿ⁾ which is a K-linear subspace for some subfield K $\subseteq$ F. As well as the basic constructions, the important class of cyclic codes are available. All significant weight distribution invariants are insatalled,

New Features:

• Invariants of an additive code, such as ambient space, alphabet, various numerical invariants, the code and dual space, can be accessed.

• Operations on code words can be carried out, e.g. arithmetic, distance and weight.

• Subcodes can be formed.

• An adaptation of the minimum weight algorithm for linear codes has been developed by Markus Grassl and Greg White for computing the minimum weight of additive codes. The runtimes for the computations are comparable to linear cods of the same cardinality.

• Constructions are provided to produce new codes from existing codes.