Linear codes over F_3 + uF_3 + u~2F_3: MacWilliams identities, optimal ternary codes from one-Lee weight codes and two-Lee weight codes

摘要

Let R = F_3 + uF_3 + u~2F_3, where u~3 = 1. Lee weights, Gray map for linear codes over R are defined in this paper, and the MacWilliams identities for complete, Hamming, symmetrized and Lee weight enumerators are verified. Moreover, the construction method of one-Lee weight codes over R with type 27~(k_1)9~(k_2)3~(k_3) is determined. By the Gray map, a family of one-weight ternary linear codes is obtained, whose parameters attain the Plotkin bound and Griesmer bound.We also obtain a class of optimal ternary codes from two-Lee weight projective codes over R, which meet the Griesmer bound. Finally, some examples are given to illustrate the results.