相关论文: An Optimal 14-Symbol Hybrid Basis for BCH-Algebras

The Boolean product $R = P \cdot Q$ of two $\{ 0, 1\} \; m \times m \; $ matrices is $$R(j,k) = 1 \; \mathrm{\ IF\ for\ some\ } \; t \; \,P(j, t) = Q(t, k) = 1\; \; \mathrm{ELSE\ } \, R(j, k) = 0. $$ The near-optimal design reduces the…

Double Boolean algebras (dBas), introduced by Wille, are based on twenty-three identities. We present a simplified axiom system, the D-core algebra, and prove it is equivalent to Wille's original definition. This reduction allows improved…

In this paper, we present a new axiomatic system that is a minimal axiomatization of Boolean algebras. Furthermore, the symmetric difference is shown to be algebraically analogous to the modular difference of two numbers. Finally, a new…

With the inclusion of an effective methodology, this article answers in detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XCB = e(x,e(e(e(x,y),e(z,y)),z)) a single…

We use computer algebra to study the 512-dimensional associative algebra Q B_3, the rational monoid algebra of 3 x 3 Boolean matrices. We obtain a basis for the radical in bijection with the 42 non-regular elements of B_3. The center of the…

Since Cocke and Minsky proved 2-tag systems universal, they have been extensively used to prove the universality of numerous computational models. Unfortunately, all known algorithms give universal 2-tag systems that have a large number of…

In the present paper we study the following problem: how to construct a coherent orthoalgebra which has only a finite number of elements, but at the same time does not admit a bivaluation (i.e. a morphism with a codomain being an…

This paper introduces an enhanced normalized min-sum decoder designed to address the performance and complexity challenges associated with developing parallelizable decoders for short BCH codes in high-throughput applications. The decoder…

Let $\mathbf{B}$ be a basis for an $r$-dimensional algebra $A$ over a field or commutative ring with unity. The semifusions of $\mathbf{B}$ are the partitions of $\mathbf{B}$ whose characteristic functions form the basis of a subalgebra of…

This article discusses the representation theory of noncommutative algebras reality-based algebras with positive degree map over their field of definition. When the standard basis contains exactly two nonreal elements, the main result…

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical…

It has long been an open question whether the formula XCB = EpEEEpqErqr is, with the rules of substitution and detachment, a single axiom for the classical equivalential calculus. This paper answers that question affirmatively, thus…

In [3] S. J. Bhatt and H. V. Dedania exposed certain classes of Banach algebras in which every element is a topological divisor of zero. We identify a new (large) class of Banach algebras with the aforementioned property, namely, the class…

The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. A subclass of attractive BCH codes is the…

We develop the bialgebra theory for two classes of non-associative algebras: nearly associative algebras and $LR$-algebras. In particular, building on recent studies that reveal connections between these algebraic structures, we establish…

In this paper, we prove that for a given biquaternion algebra over a field of characteristic two, one can move from one symbol presentation to another by at most three steps, such that in each step at least one entry remains unchanged. If…

This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in the setting of partial flag varieties of…

We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…

Discovered by Bose, Chaudhuri and Hocquenghem, the BCH family of error correcting codes are one of the most studied families in coding theory. They are also among the best performing codes, particularly when the number of errors being…

Almost difference sets have emerged as a fascinating and important area of research as they can produce functions with optimal nonlinearity, cyclic codes, and binary sequences with optimal autocorrelation. This study aims to investigate the…