HEXAGONAL METRIC FOR LINEAR CODES OVER A FINITE FIELD

This paper consider Hexagonal-metric codes over certain class of finite fields.The Hexagonal metric as defined by Huber is a non-trivial metric over certain classes of finite fields.Hexagonal-metric codes are applied in coded modulation scheme based on hexagonal-like signal consteEations.Since the development of tight bounds for error correcting codes using new distance is a research problem,the purpose of this note is to generalize the Plotkin bound for linear codes over finite fields equipped with the Hexagonal metric.By means of a two-step method,the author presents a geometric method to construct finite signal constellations from quotient lattices associated to the rings of Eisenstein-Jacobi (EJ) integers and their prime ideals and thus naturally label the constellation points by elements of a finite field.The Plotkin bound is derived from simple computing on the geometric figure of a finite field.