Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound
For coding theorists, this resolves a long-standing open problem by providing the first infinite families of self-dual binary cyclic codes exceeding the square-root bound.
This paper solves a 70-year-old open problem by constructing infinite families of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. It also produces cyclic codes with improved parameters compared to existing references.
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.