Formally Self-Dual Codes Related to Type II Codes

Shadows play an important role in the study of self-dual codes. In this note, we give constructions of formally self-dual codes using self-dual codes and their shadows. As an example, a class of binary formally self-dual codes related to extremal Type II code is introduced. This work was partially supported by the Grant-in-Aid for Scientific Research (No. 10740044), the Ministry of Education, Science, Sports and Culture, Japan, and the Sumitomo Foundation (No. 990645), Japan.Keywords:Formally self-dual codes, Type II codes and codes over _2k.     

On Type II codes over F4

Previously, Type II codes over F₄ have been introduced as Euclidean self-dual codes with the property that all Lee weights are divisible by four. In this paper, a number of properties of Type II codes are presented. We construct several extremal Type II codes and a number of extremal Type I codes. It is also shown that there are seven Type II codes of length 12, up to permutation equivalence     

Optimal self-dual codes over F/sub 2//spl times/F/sub 2/ with respect to the Hamming weight

In this paper, we study optimal self-dual codes and type IV self-dual codes over the ring F/sub 2//spl times/F/sub 2/ of order 4. We give improved upper bounds on minimum Hamming and Lee weights for such codes. Using the bounds, we determine the highest minimum Hamming and Lee weights for such codes of lengths up to 30. We also construct optimal self-dual codes and type IV self-dual codes.