Cyclotomic Constructions of Cyclic Codes With Length Being the Product of Two Primes

Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. In this paper, three types of generalized cyclotomy of order two are described and three classes of cyclic codes of length n₁ n₂ and dimension (n₁ n₂ + 1)/2 are presented and analyzed, where n₁ and n₂ are two distinct primes. Bounds on their minimum odd-like weight are also proved. Some of the codes presented in this paper are among the best cyclic codes.