Several classes of optimal

Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let p ≥ 5 be an odd prime and m b...
Ausführliche Beschreibung

Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let p ≥ 5 be an odd prime and m be a positive integer. Let C ( 1 , e , s ) denote the p-ary cyclic code with three nonzeros α, α e , and α s , where α is a generator of F p m ⁎ , s = p m − 1 2 , and 2 ≤ e ≤ p m − 2 . In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal p-ary cyclic codes C ( 1 , e , s ) with parameters [ p m − 1 , p m − 2 m − 2 , 4 ] . Some known results on optimal quinary cyclic codes with parameters [ 5 m − 1 , 5 m − 2 m − 2 , 4 ] are special cases of our constructions. In addition, by analyzing the irreducible factors of certain polynomials over F 5 m , we present two classes of optimal quinary cyclic codes C ( 1 , e , s ) . Ausführliche Beschreibung