Codes from Cocycles

We demonstrate that many techniques for generating error-correcting codes are cocyclic; that is, derived from 2-dimensional cocycles or cocyclic matrices. These cocyclic codes include classes of self-dual codes, quasi-twisted codes and, trivially, all the group ring codes and the group codes for the Gaussian channel. We believe this link between algebraic coding theory and low-dimensional group cohomology leads to (i) new ways to generate codes; (ii) a better understanding of the structure of some known codes and (iii) a better understanding of known construction techniques.

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