Janwa, Heeralal; McGuire, Gary; Wilson, Richard M. Double-error-correcting cyclic codes and absolutely irreducible polynomials over \(\text{GF}(2)\). (English) Zbl 0853.94021 J. Algebra 178, No. 2, 665-676 (1995). The paper studies the minimum distance of binary cyclic codes of length \(n = 2^s - 1\) with generator polynomial \(m_1 m_t (x)\) when \(m_i (x)\) is the minimal polynomial of \(\omega^i\) over \(GF(2)\) and \(\omega\) is a primitive element of \(GF (2^s)\). Using Weil’s theorem and Bezout’s theorem, numerical conditions are derived for the minimum distance of such a code to be greater than 4. A conjecture that would classify all such codes in terms of their minimum distance is formulated. Reviewer: V.Tonchev (Houghton) Cited in 2 ReviewsCited in 28 Documents MSC: 94B15 Cyclic codes 11T06 Polynomials over finite fields 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) Keywords:BCH codes; minimum distance; binary cyclic codes PDFBibTeX XMLCite \textit{H. Janwa} et al., J. Algebra 178, No. 2, 665--676 (1995; Zbl 0853.94021) Full Text: DOI Online Encyclopedia of Integer Sequences: Numbers of the form 2^k+1 or 4^k-2^k+1. Numbers of the form 2^k*(2^n+1) or 2^k*(4^n-2^n+1).