s-Extremal Additive Codes over GF(4)
Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F 4 , give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths (only strongly conjectured for odd d) for which there exist s-extremal codes with 5 les d les 11, and give five s-extremal codes with d = 7 as well as four new s-extremal codes with d = 5. We also describe codes related to s-extremal codes
E. P. Bautista, P. Gaborit, J. Kim and J. L. Walker, "s-Extremal Additive Codes over GF(4)," 2006 IEEE International Symposium on Information Theory, Seattle, WA, 2006, pp. 1296-1300, doi: 10.1109/ISIT.2006.262035.