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On Linear Perfect b -Symbol Codes over Finite Fields

Author

Listed:
  • Kanat Abdukhalikov

    (Department of Mathematical Sciences, UAE University, Al Ain P.O. Box 15551, United Arab Emirates)

  • Jiajie Chen

    (School of Mathematical Sciences, Peking University, Beijing 100871, China)

  • Rongquan Feng

    (School of Mathematical Sciences, Peking University, Beijing 100871, China)

Abstract

Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for b -symbol read channels where b ≥ 2 in 2016. In this paper, we establish a b -sphere-packing bound and present a recurrence relationship for the b -weight enumerator. We determine all parameters of linear perfect b -symbol e -error-correcting codes over F q for e < 2 b and show that for 2 b ≤ e < 3 b , there exist at most finite such codes for a given b , e , and q . We construct a family of linear perfect b -symbol b -error-correcting codes over F q using constacyclic codes.

Suggested Citation

  • Kanat Abdukhalikov & Jiajie Chen & Rongquan Feng, 2023. "On Linear Perfect b -Symbol Codes over Finite Fields," Mathematics, MDPI, vol. 11(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4128-:d:1251098
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