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Cyclic Codes Over\(\mathbb{Z}_{4}\) of Even Length

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Abstract

We determine the structure of cyclic codes over\(\mathbb{Z}_{4}\) for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual codes of length less than or equal to 14.

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Authors and Affiliations

  1. Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA

    Steven T. Dougherty

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Block 5, Level 3, 1 Nanyang Walk, Singapore, 637616, Republic of Singapore

    San Ling

Authors
  1. Steven T. Dougherty
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  2. San Ling
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Correspondence to Steven T. Dougherty.

Additional information

Communicated by: T. Helleseth

San Ling - The research of the second named author is partially supported by research Grants MOE-ARF R-146-000-029-112 and DSTA R-394-000-011-422.

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Dougherty, S.T., Ling, S. Cyclic Codes Over\(\mathbb{Z}_{4}\) of Even Length. Des Codes Crypt 39, 127–153 (2006). https://doi.org/10.1007/s10623-005-2773-x

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  • DOI: https://doi.org/10.1007/s10623-005-2773-x

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