Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Designs and their codes
On designs and formally self-dual codes
Designs, Codes and Cryptography
On the nonexsitence of extremal self-dual codes
Discrete Applied Mathematics
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics)
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics)
Nonexistence of near-extremal formally self-dual even codes of length divisible by 8
Discrete Applied Mathematics
Shadow bounds for self-dual codes
IEEE Transactions on Information Theory
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
Formally self-dual additive codes over F4
Journal of Symbolic Computation
Directed graph representation of half-rate additive codes over GF(4)
Designs, Codes and Cryptography
Constructing formally self-dual codes over Rk
Discrete Applied Mathematics
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A code $${\mathcal {C}}$$ is called formally self-dual if $${\mathcal {C}}$$ and $${\mathcal {C}^{\perp}}$$ have the same weight enumerators. There are four types of nontrivial divisible formally self-dual codes over $${\mathbb {F}_2,\,\mathbb {F}_3}$$ , and $${\mathbb F_4}$$ . These codes are called extremal if their minimum distances achieve the Mallows-Sloane bound. S. Zhang gave possible lengths for which extremal self-dual codes do not exist. In this paper, we define near-extremal formally self-dual (f.s.d.) codes. With Zhang's systematic approach, we determine possible lengths for which the four types of near-extremal formally self-dual codes as well as the two types of near-extremal formally self-dual additive codes cannot exist. In particular, our result on the nonexistence of near-extremal binary f.s.d. even codes of any even length n completes all the cases since only the case 8|n was dealt with by Han and Lee.