Related papers: On the permutation automorphisms of binary cubic c…

We prove that an automorphism of order 3 of a putative binary self-dual [120, 60, 24] code C has no fixed points. Moreover, the order of the automorphism group of C divides 2^a.3.5.7.19.23.29 where a is a nonegative integer. Automorphisms…

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…

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.

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…

The automorphism group of a code is the group of permutations that map a code to itself. Berman codes are a class of binary linear codes characterized by two integer parameters $n\geq 2$ and $m\geq 1$, and this class includes the…

It has been proven in a series of works that the order of the automorphism group of a binary [72,36,16] code does not exceed five. We obtain a parametrization of all self-dual binary codes of length 72 with automorphism of order 4 which can…

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…

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group $G$ of degree $n$ there exists a doubly-even self-dual $G$-invariant code if and only…

Let C be a binary linear code and suppose that its automorphism group contains a non trivial subgroup G. What can we say about C knowing G? In this paper we collect some answers to this question in the cases G=C_p, G=C_2p and G=D_2p (p an…

A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…

The existence of an extremal self-dual binary linear code C of length 72 is a long-standing open problem. We continue the investigation of its automorphism group: looking at the combination of the subcodes fixed by different involutions and…

We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by…

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…

We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F_2 + uF_2 and F_4 + uF_4; using groups of order 3, 7, 9, 13, and 15.…

The structure of binary self-dual codes invariant under the action of a cyclic group of order $pq$ for odd primes $p\neq q$ is considered. As an application we prove the nonexistence of an extremal self-dual $[96, 48, 20]$ code with an…

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…

We prove that a putative $[72,36,16]$ code is not the image of linear code over $\ZZ_4$, $\FF_2 + u \FF_2$ or $\FF_2+v\FF_2$, thus proving that the extremal doubly even $[72,36,16]$-binary code cannot have an automorphism group containing a…

Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g^p is a fixed point free involution. If C is extremal of length a multiple of 24 all the involutions are fixed point free, except the…

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72 that has an automorphism group containing D10, Z3xZ3, or Z7. Combining this with the known results in the literature one obtains that…

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72, whose automorphism group contains the symmetric group of degree 3, the alternating group of degree 4 or the dihedral group of order 8.…