Year: 2024
Type: article
Abstract: In a paper from 2015, Ding et al. (IEEE Trans. IT, May 2015) conjectured that for odd m, the minimum distance of the binary BCH code of length$2^{m}-1$and designed distance$2^{m-2}+1$is equal to the Bose distance calculated in the same paper. In this paper, we prove the conjecture. In fact, we prove a stronger result suggested by Ding et al.: the weight of the generating idempotent is equal to the Bose distance for both odd and even m. Our main tools are some new properties of the so-called fibbinary integers, in particular, the splitting field of related polynomials, and the relation of these polynomials to the idempotent of the BCH code.
Authors: Yaron Shany, Amit Berman
Institution: Samsung (Israel)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405754603