Related papers: The PBD-Closure of Constant-Composition Codes
Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a…
This paper provides a comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes of length $4p^{\varsigma}$ over the finite field $\mathbb{F}_{p^m}$, where $p$ is an odd prime number. Furthermore, it introduces…
If $S$ is a transitive metric space, then $|C|\cdot|A| \le |S|$ for any distance-$d$ code $C$ and a set $A$, ``anticode'', of diameter less than $d$. For every Steiner S$(t,k,n)$ system $S$, we show the existence of a $q$-ary…
In this paper, we analyze $m$-dimensional ($m$D) convolutional codes with finite support, viewed as a natural generalization of one-dimensional (1D) convolutional codes to higher dimensions. An $m$D convolutional code with finite support…
We examine and compare several different classes of "balanced" block codes over q-ary alphabets, namely symbol-balanced (SB) codes, charge-balanced (CB) codes, and polarity-balanced (PB) codes. Known results on the maximum size and…
Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise to optimal frequency-hopping sequences and optimal comma-free codes. New constructions for PCDPs, based on almost difference sets and cyclic difference matrices,…
The construction of Maximum Distance Profile (MDP) convolutional codes in general requires the use of very large finite fields. In contrast convolutional codes with optimal column distances maximize the column distances for a given…
Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as…
Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
Let $t \in \{2,8,10,12,14,16,18\}$ and $n=31s+t\geq 14$, $d_{a}(n,5)$ and $d_{l}(n,5)$ be distances of binary $[n,5]$ optimal linear codes and optimal linear complementary dual (LCD) codes, respectively. We show that an $[n,5,d_{a}(n,5)]$…
A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the…
A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a…
We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4),…
Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to…
Near maximum distance separable (NMDS) codes, where both the code and its dual are almost maximum distance separable, play pivotal roles in combinatorial design theory and cryptographic applications. Despite progress in fixed dimensions…