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Classification of optimal (v, k, 1) binary cyclically permutable constant weight codes with \(k=5,\) 6 and 7 and small lengths

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Abstract

We classify optimal (v, k, 1) binary cyclically permutable constant weight (CPCW) codes with small v and \(k=5, 6\) and 7. Binary CPCW codes have multiple applications in contemporary communications and are closely related to cyclic binary constant weight codes, difference packings, optical orthogonal codes, cyclic difference families and cyclic block designs. The presented small length codes can be used in relevant applications, as well as with recursive constructions for bigger lengths. We also establish that a (127, 7, 1) cyclic difference family does not exist.

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Acknowledgements

The authors are grateful to the anonymous referee whose suggestions improved the paper.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Tsonka Baicheva & Svetlana Topalova

  2. D. A. Tsenov Academy of Economics, Svishtov, Bulgaria

    Tsonka Baicheva

Authors
  1. Tsonka Baicheva
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  2. Svetlana Topalova
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Correspondence to Tsonka Baicheva.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

The research of Tsonka Baicheva was partially supported by the Bulgarian National Science Fund [Contract No. 12/8, 15.12.2017]. The research of Svetlana Topalova was partially supported by the Bulgarian National Science Fund [Contract No. DH 02/2, 13.12.2016].

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Baicheva, T., Topalova, S. Classification of optimal (v, k, 1) binary cyclically permutable constant weight codes with \(k=5,\) 6 and 7 and small lengths. Des. Codes Cryptogr. 87, 365–374 (2019). https://doi.org/10.1007/s10623-018-0534-x

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  • DOI: https://doi.org/10.1007/s10623-018-0534-x

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