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Dual codes of systematic group codes over abelian groups

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Abstract

For systematic codes over finite fields the following result is well known: If [I¦P] is the generator matrix then the generator matrix of its dual code is [ −P tr¦I]. The main result is a generalization of this for systematic group codes over finite abelian groups. It is shown that given the endomorphisms which characterize a group code over an abelian group, the endomorphisms which characterize its dual code are identified easily. The self-dual codes are also characterized. It is shown that there are self-dual and MDS group codes over elementary abelian groups which can not be obtained as linear codes over finite fields.

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    A. A. Zain & B. Sundar Rajan

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  1. A. A. Zain
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  2. B. Sundar Rajan
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Part of this correspondence was presented in 1994 International Symposium on Information Theory, Trondheim, Norway, June 1994

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Zain, A.A., Rajan, B.S. Dual codes of systematic group codes over abelian groups. AAECC 8, 71–83 (1997). https://doi.org/10.1007/s002000050054

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  • DOI: https://doi.org/10.1007/s002000050054

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