Related papers: A New Algorithm for Equivalence of Cyclic Codes an…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem…
As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…
In this paper, we construct a new family of distance-optimal binary cyclic codes with the minimum distance $6$ and a new family of distance-optimal quaternary cyclic codes with the minimum distance $4$. We also construct several families of…
We detail for the first time a complete explicit description of the quasi-cyclic structure of all classical finite generalized quadrangles. Using these descriptions we construct families of quasi-cyclic LDPC codes derived from the…
This paper is dealing with DNA cyclic codes which play an important role in DNA computing and have attracted a particular attention in the literature. Firstly, we introduce a new family of DNA cyclic codes over the ring…
This comprehensive survey examines the field of alphabetic codes, tracing their development from the 1960s to the present day. We explore classical alphabetic codes and their variants, analyzing their properties and the underlying…
Generalized Bicycle (GB) codes offer a compelling alternative to surface codes for quantum error correction. This paper focuses on (2,2)-Generalized Bicycle codes, constructed from pairs of binary circulant matrices with two non-zero…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a family of $p$-ary cyclic…
In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
We propose a new family of polar coding which realizes high coding gain, low complexity, and high throughput by introducing a protograph-based design. The proposed technique called as quasi-cyclic (QC) polar codes can be highly parallelized…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…
The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring $\mathfrak{R}$. An algorithm to find the generator polynomials of $n$ dimensional ($n$D) cyclic codes of length…
Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Perfect nonlinear monomials were employed to…