Binary cyclic codes from permutation polynomials over F2m

Abstract

Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal trade-off between these two factors, making them suitable for demanding communication and storage systems, post-quantum cryptography, radar and sonar systems, wireless sensor networks, and space communications. This paper aims to investigate cyclic codes by an efficient approach introduced by Ding [5] from several known classes of permutation monomials and trinomials over F2m. We present several infinite families of binary cyclic codes of length 2m-1 with dimens..