Some ternary and quaternary codes and associated sphere packings

Abstract

Tables of good ternary and quaternary codes are presented, and they are used in the construction of dense sphere packings. Results include (1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50; (2) a class of optimal (n, 2) codes over GF(q); (3) the (u+v+w mod 2u+v mod u) construction, a new ternary code construction technique that can be used to construct the ternary Reed-Muller codes (and others); and (4) tables of linear ternary and quaternary codes obtained by modifying and combining various codes here and in the literature. Packings are generated in even dimensions up to 100 using these codes and a sphere-packing construction. In dimensions 36 and 60, new record densities appear to have been achieved.<>