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Some cyclic codes of length 2p n

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Abstract

Explicit expressions for 4n + 2 primitive idempotents in the semi-simple group ring \(R_{2p^{n}}\equiv \frac{GF(q)[x]}{<x^{2p^{n}}-1>}\) are obtained, where p and q are distinct odd primes; n ≥ 1 is an integer and q has order \({\frac{\phi(2p^{n})}{2}}\) modulo 2p n. The generator polynomials, the dimension, the minimum distance of the minimal cyclic codes of length 2p n generated by these 4n + 2 primitive idempotents are discussed. For n = 1, the properties of some (2p, p) cyclic codes, containing the above minimal cyclic codes are analyzed in particular. The minimum weight of some subset of each of these (2p, p) codes are observed to satisfy a square root bound.

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Authors and Affiliations

  1. Department of Mathematics, T.I.T. & S., Birla Colony, Bhiwani, 127021, India

    Sudhir Batra

  2. Department of Mathematics, Maharshi Dayanand University, Rohtak, 124001, India

    S. K. Arora

Authors
  1. Sudhir Batra
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  2. S. K. Arora
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Correspondence to Sudhir Batra.

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Communicated by J. Wolfmann.

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Batra, S., Arora, S.K. Some cyclic codes of length 2p n . Des. Codes Cryptogr. 61, 41–69 (2011). https://doi.org/10.1007/s10623-010-9438-0

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  • DOI: https://doi.org/10.1007/s10623-010-9438-0

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