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Transform domain characterization of cyclic codes overZ m

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Cyclic codes with symbols from a residue class integer ringZ m are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring ofZ m . It is shown that a cyclic code of length n overZ m ,n relatively prime tom, consists ofn-tuples overZ m having a specified set of DFT coefficients from the elements of an ideal of a subring of the extension ring. Whenm is equal to a product of distinct primes every cyclic code overZ m has an idempotent generator and it is shown that the idempotent generators can be easily identified in the transform domain. The dual code pairs overZ m are characterized in the transform domain for cyclic codes. Necessary and sufficient conditions for the existence of self-dual codes overZ m are obtained and nonexistence of self-dual codes for certain values ofm is proved.

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Rajan, B.S., Siddiqi, M.U. Transform domain characterization of cyclic codes overZ m . AAECC 5, 261–275 (1994). https://doi.org/10.1007/BF01225641

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  • DOI: https://doi.org/10.1007/BF01225641

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