A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization was given in [3]. The main purpose of this work is to show that the numerical conditions found in [3], are also necessary. As we will see later, an interesting...

We define Type II codes over R = F2+uF2+uF2+uF2+....+uF2, m = 2k, k ∈ N .It is examined the existense of self dual code over R and we have the Gray images of the Type II codes over R. Mathematics Subject Classificition: 94B05

A classical result of Conway and Pless is that a natural projection of the xed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual [13]. In this paper we prove that the same holds for involutions under some (quite strong) conditions on the codes. In order to prove it, we introduce a new family of binary codes: the semi self-dual codes. A binary self-orthogo...

In this note, an extremal doubly even self-dual code of length 112 is constructed for the first time. This length is the smallest length for which no extremal doubly even self-dual code of length n 6≡ 0 (mod 24) has been constructed.

There are two distinct weight enumerators for extremal singly-even self-dual [36; 18; 8] codes. For each weight enumerator, only one extremal self-dual code is previously known. In this correspondence, we construct several new extremal singly-even self-dual [36; 18; 8] codes for each weight enumerator. We also construct a number of new extremal singly-even self-dual [38; 19; 8] codes.

The aim of this work is to study the dual and algebraic an evaluation code using standard monomials indicator functions. We show that dual. develop algorithm for computing a basis Let $C_1$ $C_2$ be linear codes spanned by monomials. give combinatorial condition monomial equivalence $C_2^\perp$. Moreover, we explicit description generator matrix $C_2^\perp$ in terms coefficients For Reed--Mulle...

Let R = Z4[u]/〈u〉 = Z4 + uZ4 + . . . + uZ4 (u = 0) where k ∈ Z satisfies k ≥ 2. For any odd positive integer n, it is known that cyclic codes over R of length n are identified with ideals of the ring R[x]/〈x − 1〉. In this paper, an explicit representation for each cyclic code over R of length n is provided and a formula to count the number of codewords in each code is given. Then a formula to c...

Let F2m be a finite field of characteristic 2 and R = F2m [u]/〈u 〉 = F2m + uF2m + . . . + u k−1 F2m (u k = 0) where k ∈ Z satisfies k ≥ 2. For any odd positive integer n, it is known that cyclic codes over R of length 2n are identified with ideals of the ring R[x]/〈x − 1〉. In this paper, an explicit representation for each cyclic code over R of length 2n is provided and a formula to count the n...

Throughout this paper all codes are assumed to be binary. A linear code C is formally self-dual (fsd) if C and its dual C have the same weight enumerator. While self-dual codes contain only even weight vectors, formally self-dual codes may contain odd weight codewords as well. Many authors consider only even formally self-dual codes because their weight enumerators are combinations of Gleason p...