Asymptotically good ZprZps-additive cyclic codes |
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Institution: | 1. Department of Mathematics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic;2. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6;1. Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People''s Republic of Korea;2. PGItech Corp., Pyongyang, Democratic People''s Republic of Korea;3. LAGA, Department of Mathematics, University of Paris VIII, 93526 Saint-Denis, France;4. University of Paris XIII, CNRS, LAGA UMR 7539, Sorbonne Paris Cite, 93430 Villetaneuse, France;5. Telecom ParisTech, 75013 Paris, France |
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Abstract: | We construct a class of -additive cyclic codes generated by pairs of polynomials, where p is a prime number. Based on probabilistic arguments, we determine the asymptotic rates and relative distances of this class of codes: the asymptotic Gilbert-Varshamov bound at is greater than and the relative distance of the code is convergent to δ, while the rate is convergent to for and . As a consequence, we prove that there exist numerous asymptotically good -additive cyclic codes. |
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Keywords: | Random codes Cumulative weight enumerator Gilbert-Varshamov bound Asymptotically good |
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