Linear Codes over Finite Rings [HB 108]

Changes:

• Codes over integer residue rings are now classified by the total number of codewords they contain. Previously they were classified by the number of generators, which was not invariant for equivalent codes.

New Features:

• Magma now supports error correcting codes over Galois rings. Constructions include CyclicCode, as well as facilities to factorize xⁿ - 1. Important structural calculations are available such as the CompleteWeightEnumerator and the Hamming WeightDistribution.
• Magma now has special functionality for codes over Z4, the ring of integers modulo 4. A host of specific constructions include KerdockCode, PreparataCode, ReedMullerCode, GoethalsCode, and more. The optimized calculations of LeeWeightDistribution and EuclideanWeightDistribution are also included. Derived binary codes can be obtained, including those from the GrayMap.