For a Type T ∈ {I, II, III, IV} and length N where there exists no self-dual Type T code of length N , upper bounds on the minimum weight of the dual code of a self-orthogonal Type T code of length N are given, allowing the notion of dual extremal codes. It is proven that the Hamming weight enumerator of a dual extremal maximal self-orthogonal code of a given length is unique.

It was shown by Gaborit el al. [10] that a Euclidean self-dual code over GF (4) with the property that there is a codeword whose Lee weight ≡ 2 (mod 4) is of interest because of its connection to a binary singly-even self-dual code. Such a self-dual code over GF (4) is called Type I. The purpose of this paper is to classify all Type I codes of lengths up to 10 and extremal Type I codes of lengt...

The binomial moments of a linear code are synonymously related to its weight distribution and appear naturally in studies involving the weight distribution of the code. In particular , the binomial moments have been used for establishing bounds on the undetected error probability and, though implicitly, for the study of good and proper codes. In this work we sharpen known bounds on the binomial...

We study odd and even Z2Z4 formally self-dual codes. The images of these codes are binary codes whose weight enumerators are that of a formally self-dual code but may not be linear. Three constructions are given for formally self-dual codes and existence theorems are given for codes of each type defined in the paper.

The notion of an extremal self-dual code has been introduced in 1 . As Gleason 2 remarks onemay use invariance properties of the weight enumerator of a self-dual code to deduce upper bounds on the minimum distance. Extremal codes are self-dual codes that achieve these bounds. The most wanted extremal code is a binary self-dual doubly even code of length 72 and minimum distance 16. One frequentl...

In this paper, we study the p-ary linear code Ck(n, q), q = ph, p prime, h 1, generated by the incidence matrix of points and k-dimensional spaces in PG(n, q). For k n/2, we link codewords of Ck(n, q) \ Ck(n, q)⊥ of weight smaller than 2qk to k-blocking sets. We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all codewords arising from small...

(1+pw)-constacyclic codes of arbitrary length over the nonprincipal ideal ring Zps + uZps are studied, where p is a prime, w ∈ Z × ps and s an integer satisfying s ≥ 2. First, the structure of any (1 + pw)constacyclic code over Zps +uZps are presented. Then enumerations for the number of all codes and the number of codewords in each code, and the structure of dual codes for these codes are give...

Additive cyclic codes over Galois rings were investigated in [3]. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in [3], whereas the other one has some unusual propertie...

We show that there is no [24, 12, 9] doubly-even self-dual code over F4 by attempting to construct the generator matrix of this code directly.

The matroid associated to a linear code is the representable matroid that is defined by the columns of any generator matrix. The matroid associated to a self-dual code is identically self-dual, but it is not known whether every identically self-dual representable matroid can be represented by a self-dual code. This open problem was proposed in [8], where it was proved to be equivalent to an ope...