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In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…

Information Theory · Computer Science 2017-06-23 Long Yu , Xiusheng Liu

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

Category Theory · Mathematics 2015-07-24 Wolfgang Bertram

In this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree $n$ over a finite field and their roots in the extension field in quasilinear where $N=n^2$…

Discrete Mathematics · Computer Science 2016-08-12 Nader H. Bshouty , Nuha Diab , Shada R. Kawar , Robert J. Shahla

A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…

Information Theory · Computer Science 2015-03-24 Cunsheng Ding

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $\mathbb{F}_q$ having large minimum weights for $q \in \{2,3\}$. Using the characterization, we…

Combinatorics · Mathematics 2021-01-05 Makoto Araya , Masaaki Harada , Ken Saito

In the work are defined the concepts semi-canonical and canonical binary matrix. What is described is an algorithm solving the combinatorial problem for finding the semi-canonical matrices in the set \Lambda_n^k consisting of all n\times n…

Data Structures and Algorithms · Computer Science 2014-04-28 Krasimir Yordzhev

In Part I of this series we described three algorithms that construct canonical tree-decompositions of graphs which distinguish all their k-blocks and tangles of order k. We now establish bounds on the number of parts in these…

Combinatorics · Mathematics 2014-04-25 Johannes Carmesin , Reinhard Diestel , Matthias Hamann , Fabian Hundertmark

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear…

Classical Analysis and ODEs · Mathematics 2011-04-19 Muhammad Safdar , Asghar Qadir , Sajid Ali

In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…

Information Theory · Computer Science 2014-08-14 Homa Esfahanizadeh , Farshad Lahouti , Babak Hassibi

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…

Classical Analysis and ODEs · Mathematics 2007-12-27 F. M. Mahomed , A. Qadir

We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…

Combinatorics · Mathematics 2024-06-25 Aida Abiad , Alexander L. Gavrilyuk , Antonina P. Khramova , Ilia Ponomarenko

We study a new class of codes over Z_2 x Z_2 which we call L-codes. They arise as a natural fifth step in a series of analogies between Kleinian codes, binary codes, lattices and vertex operator algebras. This analogy will be explained in…

Combinatorics · Mathematics 2010-08-12 Julia Galstad , Gerald Hoehn

We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.

Algebraic Geometry · Mathematics 2009-04-09 Takafumi Shibuta , Shunsuke Takagi

We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.

Optimization and Control · Mathematics 2012-05-01 Walter D. Morris

We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensions. This approach is different from earlier approaches…

Information Theory · Computer Science 2024-05-30 Ferruh Ozbudak , Paolo Santonastaso , Ferdinando Zullo

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…

Symbolic Computation · Computer Science 2012-10-23 Changbo Chen , Marc Moreno Maza

A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected…

Information Theory · Computer Science 2014-09-09 Chao Chen

Multi-label text classification (MLC) is a challenging task in settings of large label sets, where label support follows a Zipfian distribution. In this paper, we address this problem through retrieval augmentation, aiming to improve the…

Computation and Language · Computer Science 2023-05-23 Ilias Chalkidis , Yova Kementchedjhieva

We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.

Logic in Computer Science · Computer Science 2010-09-16 Anders Schack-Nielsen , Carsten Schürmann

Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…

Information Theory · Computer Science 2015-05-27 Can Xiang , Hao Liu