MAGMA Computational Algebra System

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Linear Codes over Finite Rings

New Features:

• A package, developed by J. Pernas, J. Pujol and M. Villanueve, that extends the existing facilities in Magma for codes over the ring Z₄ is included.

• Constructions are given for families of codes, including Hadamard codes and Reed-Muller codes: HadamardCodeZ4, ExtendedPerfactCodeZ4, Reed-MullerCodeZ4, Reed-MullerCodeQRZ4,
  Reed-MullerCodeLRMZ4, and Reed-MullerCodeMZ4.

• Another group of functions produce new Z₄-codes by modifying in some way the code words of given Z₄-codes. This includes the functions PlotkinSum, QuaternaryPlotkinSum, BQPlotkinSum, DoublePlotkinSum, and DualKronecker.

• Functions are provided which compute the rank and dimension of the kernel of any code over Z₄. The functions are:- SpanZ2CodeZ4, KernelZ2CodeZ4, DimensionOfSpanZ2, DimensionOfKernelZ2.