Related papers: On Codes based on BCK-algebras
We show that the variety of MV-algebras is $2$-based and we offer elegant $2$-bases for the varieties of commutative BCK-algebras and {\L}BCK-algebras.
This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that…
We define and study a new class of bialgebras, which generalize certain Turner double algebras related to generic blocks of symmetric groups. Bases and generators of these algebras are given. We investigate when the algebras are symmetric,…
In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilistic reasoning. We present a relation between state operators…
In this short survey we concern ourselves with minimal codes, a classical object in coding theory. We will explain the relation between minimal codes and various other mathematical domains, in particular with finite projective geometry.…
The class of weak BCK-algebras is obtained by weakening one of standard BCK axioms. It is known that every weak BCK-algebra is completely determined by the structure of its initial segments. We review several natural classes of commutative…
In this paper we propose a new class of spatially coupled codes based on repeat-accumulate protographs. We show that spatially coupled repeat-accumulate codes have several advantages over spatially coupled low-density parity-check codes…
We examine and compare several different classes of "balanced" block codes over q-ary alphabets, namely symbol-balanced (SB) codes, charge-balanced (CB) codes, and polarity-balanced (PB) codes. Known results on the maximum size and…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
Binary self-orthogonal codes and balanced incomplete block designs are two combinatorial configurations that have been much studied because of their wide areas of application. In this paper, we have shown the distribution of (16; 6;…
We study the class of structures that, in a way, generalize various approaches to the contact relation on Boolean algebras.
We present a new numerical code developed for the evolution of binary black-hole spacetimes using different initial data and evolution techniques. The code is demonstrated to produce state-of-the-art simulations of orbiting and inspiralling…
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
We consider the joint design of polar coding and higher-order modulation schemes for ever increased spectral efficiency. The close connection between the polar code construction and the multi-level coding approach is described in detail.…
We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…
Using a clear and straightforward approach, we discover and prove new binary digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. Numerous…