Related papers: Some new bounds on LCD codes over finite fields
Linear complementary dual (LCD) codes, which is a class of linear codes introduced by Massey, have been extensively studied in literature recently. It has been shown that LCD codes can help to improve the security of the information…
The length function $\ell_2(r,R)$ is the smallest length of a binary linear code with codimension (redundancy) $r$ and covering radius $R$. We obtain the following new upper bounds on $\ell_2(r,R)$, which yield a decrease $\Delta(r,R)$…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
In this paper we investigate known Singleton-like bounds in the Lee metric and characterize optimal codes, which turn out to be very few. We then focus on Plotkin-like bounds in the Lee metric and present a new bound that extends and…
In this paper we carefully study the MSE performance of the linear analog codes. We have derived a lower bound of the MSE performance under Likelihood(ML) and Linear Minimal Mean Square Error(LMMSE) decoding criteria respectively. It is…
An $L$-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set $L$. We show, for a fixed $\alpha,\beta>0$, that the size of any $[-1,-\beta]\cup\{\alpha\}$-spherical code is at most linear in the…
We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…
An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is…
In this paper, we first introduce the extended binary representation of non-binary codes, which corresponds to a covering graph of the bipartite graph associated with the non-binary code. Then we show that non-binary codewords correspond to…
Self-dual cyclic codes form an important class of linear codes. It has been shown that there exists a self-dual cyclic code of length $n$ over a finite field if and only if $n$ and the field characteristic are even. The enumeration of such…
We construct two series of linear codes over finite ring $\mathbb{F}_{q}[x]/(x^2)$ and Galois ring $GR(p^2,m)$ respectively reaching the Griesmer bound. They derive two series of codes over finite field $\mathbb{F}_{q}$ by Gray map. The…
Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space…
Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…
We propose an algorithm to find a lower bound for the number of cyclic codes over any finite field with any given exponent. Besides, we give a formula to find the exponent of BCH codes.
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate $\epsilon$-close to capacity, and aim to bound the dependence of the output list size $L$ on $\epsilon$,…
We study the largest possible length $B$ of $(B-1)$-dimensional linear codes over $\mathbb{F}_q$ which can correct up to $t$ errors taken from a restricted set $\mathcal{A}\subseteq \mathbb{F}_q^*$. Such codes can be applied to multilevel…