Abstract
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 constellations. 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.
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This research is supported by 973 project under Grant No. 2007CB807901 and the Fundamental Research Funds for the Central Universities under Grant Nos. YWF-10-02-072 and YWF-10-01-A28.
This paper was recommended for publication by Editor Xiao-Shan GAO.
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Gao, Y. Hexagonal metric for linear codes over a finite field. J Syst Sci Complex 24, 593–603 (2011). https://doi.org/10.1007/s11424-011-9049-5
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DOI: https://doi.org/10.1007/s11424-011-9049-5