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Optimal binary codes from one-lee weight codes and two-lee weight projective codes over ℤ4

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Abstract

This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over ℤ4. The authors first give the Pless identities on the Lee weight of linear codes over ℤ4. Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively, the construction methods of one-Lee weight and two-Lee weight projective codes over ℤ4 are also given. Finally, the authors recall the weight-preserving Gray map from (ℤ n4 , Lee weight) to (\(\mathbb{F}_2^{2n} \), Hamming weight), and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes, which reach the Plotkin bound and the Griesmer bound.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Minjia Shi

  2. Department of Mathematics and Physics, Hefei University, Hefei, 230601, China

    Yu Wang

Authors
  1. Minjia Shi
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  2. Yu Wang
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Corresponding author

Correspondence to Yu Wang.

Additional information

The first author of this paper is supported by the National Natural Science Foundation of China under Grant Nos. 61202068 and 11126174, Talents youth Fund of Anhui Province Universities under Grant No. 2012SQRL020ZD; The second author of this paper is supported by Key Discipline Construction of Hefei University 2014XK08.

This paper was recommended for publication by Editor HU Lei.

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Shi, M., Wang, Y. Optimal binary codes from one-lee weight codes and two-lee weight projective codes over ℤ4 . J Syst Sci Complex 27, 795–810 (2014). https://doi.org/10.1007/s11424-014-2188-8

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  • DOI: https://doi.org/10.1007/s11424-014-2188-8

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