Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound
2026-06-01 • Information Theory
Information Theory
AI summaryⓘ
The authors address a long-standing question in coding theory about whether there can be self-dual binary cyclic codes with minimum distances better than the previously known square-root bound. They successfully construct infinite families of such codes, thus solving the problem that has been open for 70 years. Along the way, they also create new families of cyclic codes with improved parameters compared to some earlier works.
self-dual codesbinary cyclic codesminimum distancesquare-root boundcoding theoryinfinite familieserror-correcting codescode parameters
Authors
Xiaoqiang Wang, Xun Song, Dabin Zheng, Hao Chen, Cunsheng Ding
Abstract
In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. IT, vol. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory by presenting infinite families of such self-dual binary cyclic codes. As by-products, several families of cyclic codes with better parameters than those in some references are also constructed in this paper.