Abstract
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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Horadam, K.J., Perera, A.A.I. (1997). Codes from cocycles. In: Mora, T., Mattson, H. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1997. Lecture Notes in Computer Science, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63163-1_12
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DOI: https://doi.org/10.1007/3-540-63163-1_12
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