Classification of extremal and $s$-extremal binary self-dual codes of length 38

In this paper we classify all extremal and $s$-extremal binary self-dual codes of length 38. There are exactly 2744 extremal $[38,19,8]$ self-dual codes, two $s$-extremal $[38,19,6]$ codes, and 1730 $s$-extremal $[38,19,8]$ codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. The classification of $s$-extremal $[38,19,6]$ codes permits to achieve the classification of all $s$-extremal codes with d=6.

💡 Research Summary

The paper presents a complete classification of binary self‑dual codes of length 38 that are either extremal (minimum distance 8) or s‑extremal (minimum distance 6 or 8 with a shadow of maximal possible weight). The authors build on the recent exhaustive classification of all binary self‑dual