One of the main weakness of the family of centralizer codes is that its length is always n. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form nk. We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a specia...

The weight distribution of a Goppa code is proven to be “close” to the binomial weight distribution found in a random linear code. Some bounds have been found on the distance between the two distributions and this distance is incredibly small for some particular weights. However, for smaller weights the bound on the distance is of no use. Using an algorithm to find words of minimal weight we we...

In this article we shall prove that, for q = p prime and roughly 3 8 -th’s of the values of d < q k−1, there is no linear code meeting the Griesmer bound. This result uses Blokhuis’ theorem on the size of a t-fold blocking set in PG(2, p), p prime, which we generalise to higher dimensions. We also give more general lower bounds on the size of a t-fold blocking set in PG(δ, q), for arbitrary q a...

Constructions of nonlinear covering codes are given. Using any nonlinear starting code of covering radius R 2 these constructions form an infinite family of codes with the same covering radius. A nonlinear code is treated as a union of cosets of a linear code. New infinite families of nonlinear covering codes are obtained. Concepts of R; l-objects, R; l-partitions, and R; l-length are described...

Alisrruct-Linear block codes are studied for improving the reliability of message storage in computer memory with stuck-at defects and noise. The case when the side information about the state of the defects is available to the decoder or to the encoder is considered. In the former case, stuck-at cells act as erasures so that techniques for decoding linear block codes for erasures and errors ca...

We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F2+uF2+vF2+uvF2 of length 6 and size 212. Writing a typical generating matrix of the form [I3|A], with A being a 3× 3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the gene...

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. It was proved that asymptotically good Hermitian LCD codes exist. The objective of this paper is to construct some cyclic Hermitian LCD codes over finite fields and analyse their parameters. The dimensions of these codes ar...

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...

Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...