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In this paper, we study quasi-twisted codes and their relationship with additive constacyclic codes through a polynomial-based approach. We first present a polynomial characterization of quasi-twisted codes over finite fields analogous to…
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the $q$-analogues of projective systems and blocking sets. We also illustrate how to associate a classical…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius $t=1$ or dimension $n=1, 2$. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the…
We introduce quasi-cyclic codes of index 1.5, construct such codes in terms of polynomials and matrices; and prove that the quasi-cyclic codes of index 1.5 are asymptotically good.
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…
We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
We introduce a new decomposition of a graphs into quasi-4-connected components, where we call a graph quasi-4-connected if it is 3-connected and it only has separations of order 3 that remove a single vertex. Moreover, we give a cubic time…
New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…
We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration…
Coding theory and combinatorial $t$-designs have close connections and interesting interplay. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. As we all known, some…
In this paper, we identify many important properties and develop criteria for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of subquasigroup of…
Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar\'{e} (2003). In order to obtain asymptotic approximations to their…
We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which…
We define a triangle design as a partition of the set of lines of a projective space into triangles, where a triangle consists of three pairwise intersecting lines with no common point. A triangle design is balanced if all points are…
This paper introduces a novel approach to enumerate and assess Trapping sets in quasi-cyclic codes, those with circulant sizes that are non-prime numbers. Leveraging the quasi-cyclic properties, the method employs a tabular technique to…