Related papers: On Skew Convolutional and Trellis Codes
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to…
The new method for Reed-Solomon codes decoding is introduced. The method is based on the star trellis decoding of the binary image of Reed-Solomon codes.
In this paper we propose a matched encoding (ME) scheme for convolutionally encoded transmission over intersymbol interference (usually called ISI) channels. A novel trellis description enables to perform equalization and decoding jointly,…
The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming…
This paper introduces Claycode, a novel 2D scannable code designed for extensive stylization and deformation. Unlike traditional matrix-based codes (e.g., QR codes), Claycodes encode their message in a tree structure. During the encoding…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of…
We achieve new results on skew polynomial rings and their quotients, including the first explicit example of a skew polynomial ring where the ratio of the degree of a skew polynomial to the degree of its bound is not extremal. These methods…
In this paper we propose a matched decoding scheme for convolutionally encoded transmission over intersymbol interference (ISI) channels and devise a nonlinear trellis description. As an application we show that for coded continuous phase…
The most famous error-decoding algorithm for convolutional codes is the Viterbi algorithm. In this paper, we present a new reduced complexity version of this algorithm which can be applied to a class of binary convolutional codes with…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the…
This paper presents a comprehensive guide to designing minimal trellises for both non-degenerate and degenerate decoding of quantum stabilizer codes. For non-degenerate decoding, various strategies are explored, leveraging insights from…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
The structure of multivariate semisimple codes over a finite chain ring $R$ is established using the structure of the residue field $\bar R$. Multivariate codes extend in a natural way the univariate cyclic and negacyclic codes and include…
Let $R$ be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size $2n$ and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when ${\rm…
Maximum distance separable convolutional codes are characterized by the property that the free distance reaches the generalized Singleton bound, which makes them optimal for error correction. However, the existing constructions of such…
Neural codes, represented as collections of binary strings called codewords, are used to encode neural activity. A code is called convex if its codewords are represented as an arrangement of convex open sets in Euclidean space. Previous…