Related papers: New self-dual codes of length 72
In this paper, we present a new bordered construction for self-dual codes which employs $\lambda$-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring…
In this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative Frobenius rings. By applying these techniques over different…
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…
In this paper, we introduce and investigate the neighborhood of binary self-dual codes. We prove that there is no better Type I code than the best Type II code of the same length. Further, we give some new necessary conditions for the…
A complete classification of binary self-dual codes of length 36 is given.
In this note, we demonstrate that every binary doubly even self-dual code of length $40$ can be realized as the residue code of some extremal Type II $\mathbb{Z}_4$-code. As a consequence, it is shown that there are at least $94356$…
In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereby this construction can yield self-dual codes. We construct…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
A triply even code is a binary linear code in which the weight of every codeword is divisible by 8. We show how two doubly even codes of lengths m_1 and m_2 can be combined to make a triply even code of length m_1+m_2, and then prove that…
All binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 are classified. In this way we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.
In this work, we introduce new construction methods for self-dual codes using a Baumert-Hall array. We apply the constructions over the alphabets F_2 and F_4 + uF_4 and combine them with extension theorems and neighboring constructions. As…
For lengths $36$, $48$ and $60$, we construct new ternary near-extremal self-dual codes with weight enumerators for which no ternary near-extremal self-dual codes were previously known to exist.
We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order $p \geq…
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…
A classification of extremal double circulant self-dual codes of lengths up to $88$ is known. We give a classification of extremal double circulant self-dual codes of lengths $90,92,94$ and $96$. We also classify double circulant self-dual…
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…
In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F_2^m+uF_2^m for m = 1, 2. The duality and distance preserving…
Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number we have classified all binary self-dual codes with length 76 having minimum distance $d=14$ and automorphism of order 9. Up to…
Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes,…
We investigate the properties of binary linear codes of even length whose permutation automorphism group is a cyclic group generated by an involution. Up to dimension or co-dimension $4$, we show that there is no quasi group code whose…