Formally self-dual codes over F₂[u]/‹u⁴›

In this work, Gray images of formally self-dual codes over the ring S₄ = F₂[u]/‹u⁴› and some of their construction methods are considered. As a result, a considerable number of good formally self-dual binary codes with large automorphism groups have been obtained from the Gray images of formally self-dual codes over S₄. Some have better minimum distances than the best known binary self-dual codes of the same lengths.Publisher's Versio

Generalization of the lee weight to Ζpᵏ

We introduce a new extension of the Lee weight to Ζpᵏ and later to Galois rings GR(pᵏ,m). The weight we define is a non-homogeneous weight and is different than the one that is generally labeled as "generalized Lee weight". Unlike the case of generalized Lee weight, we define a distance-preserving Gray map from (Ζpᵏ, extended Lee distance)to (Fppᵏ⁻¹, Hamming distance), thus making our extension practical for coding theory purposes.Publisher's Versio