Linear Codes over Finite Rings (New) [HB 98]

Magma now has facilities for linear codes defined over $\mbox{\bf Z}_4$. These facilities are currently basic but will be extended in the near future. Codes over general finite rings (including Galois rings) will also be supported in the future.

Features:

• Various generic constructions and functions for $\mbox{\bf Z}_4$-codes.
• Construction of cyclic codes from factorizations of xⁿ-1 over $\mbox{\bf Z}_4$.
• Standard form of a $\mbox{\bf Z}_4$-code, giving the abelian group structure.
• The Gray map and a function to test whether the image of a $\mbox{\bf Z}_4$-code under the Gray map is linear.
• Minimum weight and weight distribution.
• Weight enumerators: complete, symmetric, Lee and Hamming.
• Construction of Kerdock and Preparata codes.