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Quasi-perfect lee codes of radius 2 and arbitrarily large dimension

Abstract: A construction of two-quasi-perfect Lee codes is given over the space ?np for p prime, p ? ±5 (mod 12), and n = 2[p/4]. It is known that there are infinitely many such primes. Golomb and Welch conjectured that perfect codes for the Lee metric do not exist for dimension n ? 3 and radius r ? 2. This conjecture was proved to be true for large radii as well as for low dimensions. The codes found are very close to be perfect, which exhibits the hardness of the conjecture. A series of computations show that related graphs are Ramanujan, which could provide further connections between coding and graph theories.

 Fuente: IEEE Transactions on Information Theory, 2016, 62(3), 1183 - 1192

 Editorial: Institute of Electrical and Electronics Engineers Inc.

 Fecha de publicación: 01/03/2016

 Nº de páginas: 14

 Tipo de publicación: Artículo de Revista

 DOI: 10.1109/TIT.2016.2517069

 ISSN: 0018-9448,1557-9654

 Proyecto español: TIN2013-46957-C2-2-P

 Url de la publicación: https://doi.org/10.1109/TIT.2016.2517069