Classification of the extremal formally self-dual even codes of length 30

Nonexistence of near-extremal formally self-dual even codes of length divisible by 8

It is a well known fact that if C is an [n, k, d] formally self-dual even code with n > 30, then d ≤ 2[n/8]. A formally self-dual even code with d = 2[n/8] is called nearextremal. Kim and Pless [9] conjecture that there does not exist a near-extremal formally self dual even (not Type II) code of length n ≥ 48 with 8|n. In this paper, we prove that if n ≥ 72 and 8|n, then there is no near-extrem...

Binary extremal self-dual codes of length 60 and related codes

We give a classification of four-circulant singly even self-dual [60, 30, d] codes for d = 10 and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct extremal singly even self-dual [58...

The nonexistence of near-extremal formally self-dual codes

A code C is called formally self-dual if C and C⊥ have the same weight enumerators. There are four types of nontrivial divisible formally self-dual codes over F2, F3, and F4. These codes are called extremal if their minimum distances achieve the MallowsSloane bound. S. Zhang gave possible lengths for which extremal self-dual codes do not exist. In this paper, we define near-extremal formally se...

Classification of Extremal Formally Self-Dual Even Codes of Length 22

A note on formally self-dual even codes of length divisible by 8

A binary code with the same weight distribution as its dual code is called formally self-dual (f.s.d.). We only consider f.s.d. even codes (codes with only even weight codewords). We show that any formally self-dual even binary code C of length n not divisible by 8 is balanced. We show that the weight distribution of a balanced near-extremal f.s.d. even code of length a multiple of 8 is unique....