Related papers: Good iso-dual AG-codes from towers of function fie…
We study the fundamental problem of reliable interactive communication over a noisy channel. In a breakthrough sequence of papers published in 1992 and 1993, Schulman gave non-constructive proofs of the existence of general methods to…
Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Up until now, it was recognized that a large number of 2-torsion points was a technical barrier to improve the bounds for the symmetric tensor rank of multiplication in every extension of any finite field. In this paper, we show that there…
We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of…
We prove that the bounded and bounded below derived categories of (all) modules over the dual numbers have strongly unique (dg) enhancements. To this end we relate those categories to the category of sequences of vector spaces, which allows…
A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A code over a finite field F is a metacyclic code if it is a left ideal in the group algebra FG for G a metacyclic group. Metacyclic codes are…
Locally repairable codes have been investigated extensively in recent years due to practical application in distributed storage as well as theoretical interest. However, not much work on asymptotical behavior of locally repairable codes has…
We introduce - as a generalization of cyclic codes - the notion of transitive codes, and we show that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F_q, for all…
Motivated by a concept studied in [1], we consider a property of matrices over finite fields that generalizes triangular totally nonsingular matrices to block matrices. We show that (1) matrices with this property suffice to construct good…
We study the asymptotic behavior of double and four circulant codes, which are quasi-cyclic codes of index two and four respectively. Exact enumeration results are derived for these families of codes with the prescribed hull dimension.…
Locally repairable codes have been extensively investigated due to practical applications in distributed and cloud storage systems in recent years. However, not much work on asymptotic behavior of locally repairable codes has been done. In…
I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy…
MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field $F_q$ is completely solved for $q$ is…
This is the first in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In this work, we obtain sharp asymptotics for the probability of this "hard-wall…
We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.
Many generator matrices for constructing extremal binary self-dual codes of different lengths have the form G=(I|A), where I is the n by n identity matrix and A is the n by n matrix fully determined by the first row. In this work, we define…
We introduce two new types of towers of Drinfeld modular curves. These towers originate from a specific domain $\mathcal{A} $ and are analogous to the towers of rank-two Drinfeld modular curves over the polynomial ring. Specifically, the…
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].…
In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For some fixed $q$, our results can produce more classes of MDS…