Related papers: There exists no self-dual [24,12,10] code over F5
New $s$-extremal extremal unimodular lattices in dimensions $38$, $40$, $42$ and $44$ are constructed from self-dual codes over $\mathbb{F}_5$ by Construction A. In the process of constructing these codes, we obtain a self-dual $[44,22,14]$…
Currently, the existence of an extremal singly even self-dual code of length $24k+10$ is unknown for all nonnegative integers $k$. In this note, we study singly even self-dual $[24k+10,12k+5,4k+2]$ codes. We give some restrictions on the…
It is shown that the residue code of a self-dual $\mathbb{Z}_4$-code of length $24k$ (resp.\ $24k+8$) and minimum Lee weight $8k+4 \text{ or }8k+2$ (resp.\ $8k+8 \text{ or }8k+6$) is a binary extremal doubly even self-dual code for every…
It is known that there is no extremal singly even self-dual $[n,n/2,d]$ code with minimal shadow for $(n,d)=(24m+2,4m+4)$, $(24m+4,4m+4)$, $(24m+6,4m+4)$, $(24m+10,4m+4)$ and $(24m+22,4m+6)$. In this paper, we study singly even self-dual…
Ternary self-dual codes have been classified for lengths up to 20. At length 24, a classification of only extremal self-dual codes is known. In this paper, we give a complete classification of ternary self-dual codes of length 24 using the…
We construct new $s$-extremal singly even self-dual codes of minimum weights $8,10,12$ and $14$. We also give tables for the currently known results on the existence of $s$-extremal singly even self-dual codes of minimum weights $8,10,12$…
In this note, we construct new doubly even self-dual codes having minimum weight $20$ for lengths $112$, $120$ and $128$. This implies that there are at least three inequivalent extremal doubly even self-dual codes of length $112$.
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We…
The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with…
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…
For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z4-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed…
The existence of optimal binary self-dual codes is a long-standing research problem. In this paper, we present some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group $D_{2p}$, where $p$ is a…
Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all…
The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot occur. Supposing the…
This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
In this short note, we report the classification of self-dual $\mathbb{Z}_k$-codes of length $n$ for $k \le 24$ and $n \le 9$.
Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes.…
For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly…
The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c,f) with p…