On Linear Perfect b -Symbol Codes over Finite Fields

Kanat Abdukhalikov (), Jiajie Chen and Rongquan Feng
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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

Mathematics, 2023, vol. 11, issue 19, 1-13

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.

Keywords: b-symbol code; b-weight; b-distance; b-sphere-packing bound; perfect b-symbol code (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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