Constacyclic Codes and Cocycles
نویسنده
چکیده
Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n. In particular this isomorphism holds in many local rings (for example Galois rings) and also in the the modular ring Zr. When R is local, if n = 1 the transformation is a discrete Fourier transform, while for general n, when R is a principal ideal ring it is equivalent to the Chinese Remainder Theorem.
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