ON BINARY EXTREMAL FORMALLY SELF-DUAL EVEN CODES

On self-dual doubly-even extremal codes

Let C be a binary linear self-dual doubly-even code of length n and minimal weight d. Such codes exist only if 12 = 0 (mod 8). We put II = 24r + 8s, s = 0, 1, 2. It follows from the work of Gleason [2] and of Mallows and Sloane [6] that d s 4r + 4. C is called extremal if d = 4r + 4. In the following, an extremal code means a binary linear self-dual doubly-even extremal code. We use the set-the...

On binary self-dual extremal codes

There is a large gap between Zhang’s theoretical bound for the length n of a binary extremal self-dual doublyeven code and what we can construct. The largest n is 136. In order to find examples for larger n a non-trivial automorphism group might be helpful. In the list of known examples extended quadratic residue codes and quadratic double circulant codes have large automorphism groups. But in ...

Binary Optimal Odd Formally Self-Dual Codes

In this paper, we study binary optimal odd formally self-dual codes. All optimal odd formally self-dual codes are classified for length up to 16. The highest minimum weight of any odd formally self-dual codes of length up to 24 is determined. We also show that there is a unique linear code for parameters [16, 8, 5] and [22, 11, 7], up to equivalence.

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...

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