We shall derive a new non-trivial upper bound for the dimension of trace codes connected to algebraicgeometric codes. Furthermore, we shall deduce their true dimension if certain conditions are satisfied.

Subspace designs are a (large) collection of high-dimensional subspaces {Hi} of Fq such that for any low-dimensional subspace W , only a small number of subspaces from the collection have non-trivial intersection with W ; more precisely, the sum of dimensions of W ∩Hi is at most some parameter L. The notion was put forth by Guruswami and Xing (STOC’13) with applications to list decoding variant...

An optimal constant-composition or constant-weight code of weight has linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper ...

Abstract In 2006, K. Feng, L. Xu and F. J. Hickernell initiated the concept of a linear error-block code which is a natural generalization of the classical linear code. In this correspondence, we investigate optimal linear errorblock codes in two directions: maximal dimension codes and maximal minimum π-distance codes. First perspective on optimizing a code is by studying lower bounds and upper...

In this paper we determine completely the structure of linear codes over Z/NZ of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, and Euclidean weight. We prove a general uniqueness theorem for virtual linear codes of constant...

In this paper we study flag codes of maximum distance. We characterize these in terms of, at most, two relevant constant dimension naturally associated to them. do first for general and then particularize those arising as orbits under the action arbitrary subgroups linear group. provide different systematic orbital constructions attaining both distance size. To end, use Singer groups take advan...

Let p be an odd prime and q be a power of p. A linear [n, k, d] code over the finite field Fq is a k-dimensional subspace of F n q with minimum Hamming distance d. Let Ai denote the number of codewords with Hamming weight i in a linear code C of length n. The weight enumerator of C is defined by 1 + A1X + A2X 2 + · · ·+ AnX. The sequence (1, A1, · · · , An) is called the weight distribution of ...

We construct a large number of record-breaking binary, ternary and quaternary codes. Our methods involve the study of BCH-codes over larger fields, concatenation, construction X and variants of the Griesmer construction (residual codes). 1 Review of the theory Let IFq be the ground field, F = IFq2 . Denote the interval {i, i + 1, . . . , j} ⊂ ZZ/(q−1)ZZ by [i, j]. Let A = [i, j] ⊂ ZZ/(q−1)ZZ. I...

We give an algorithm for generating cyclic self-orthogonal (CSO) codes for an arbitrary positive integer n with gcd(n; q) = 1. Given a cyclic q-ary code of length n, we determine how many codes isomorphic to the given code are cyclic. We introduce a mass formula for CSO(n; q) codes of maximum dimension. Using the mass formula we classify CSO(63; 2) codes. This mass formula works for any cyclic ...