Related papers: Outer Strong Blocking Sets
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…
Strong difference families of special types are introduced to produce new relative difference families from the point of view of both asymptotic existences and concrete examples. As applications, group divisible designs of type $30^u$ with…
We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and…
To decode a short linear block code, ordered statics decoding (OSD) and/or the $A^*$ decoding are usually considered. Either OSD or the $A^*$ decoding utilizes the magnitudes of the received symbols to establish the most reliable and…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
The study of codes for powerlines communication has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the…
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…
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…
A $t$-fold blocking set of the finite Desarguesian plane $\mathrm{PG}(2,p^n)$, $p$ prime, is a set of points meeting each line of the plane in at least $t$ points. The minimum size of such sets is of interest for numerous reasons; however,…
The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic…
Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. Fundamental bounds, some explicit or…
A $(v,k,t)$ {\em covering design}, or {\em covering}, is a family of $k$-subsets, called blocks, chosen from a $v$-set, such that each $t$-subset is contained in at least one of the blocks. The number of blocks is the covering's {\em size},…
The study of subblock-constrained codes has recently gained attention due to their application in diverse fields. We present bounds on the size and asymptotic rate for two classes of subblock-constrained codes. The first class is binary…
In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation-discarding technique is proposed along with the stopping rule to significantly…
In this paper, we propose a new method to bound the capacity of checkerboard codes on the hexagonal lattice. This produces rigorous bounds that are tighter than those commonly known.
We present an standard constraints generation algorithm to find an explicit set whose robustness is equal to the robustness of the feasible solution set of a combinatorial optimization problem with cost uncertainty. Computational experience…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…