Another infinite family of binary cyclic codes with best parameters known

Cyclic codes are important in theory, as they are closely related to a number of areas of mathematics. Cyclic codes are also important in practice, as they have efficient encoding and decoding algorithms. An infinite family of cyclic codes over GF(q) is said to have linearly-best-known parameters if for any [n,k,d] code C in this family, there is no known [n, k, d′] linear code over GF(q) such that d′ > d. An infinite family of cyclic codes over GF(q) is said to have cyclicly-best-known parameters if for any [n, k, d] code C in this family, there is no known [n, k, d′] cyclic code over GF(q) such that d′ > d. It is very rare to see an infinite family of binary cyclic codes with cyclicly-best-known parameters whose duals codes have also cyclicly-best-known parameters. The objective of this paper is to study such family of binary cyclic codes of length 2m – 1 and dimension 2m – 1 – m(m – 1)/2, denoted by C (2,m,2), and their dual codes C⊥ (2,m,2). The weight distribution of C⊥ (2,m,2) is settled and the parameters of C(2,m,2) are investigated in this paper. A larger family of binary cyclic codes C(2,m,r) and their duals are also constructed and studied in this paper, where 0 ≤ r ≤ m – 1. IEEE