Zobrazeno 1 - 10
of 531
pro vyhledávání: '"SHI, MINJIA"'
For an integer $s\ge 1$, let $\mathcal{C}_s(q_0)$ be the generalized Zetterberg code of length $q_0^s+1$ over the finite field $\F_{q_0}$ of odd characteristic. Recently, Shi, Helleseth, and \"{O}zbudak (IEEE Trans. Inf. Theory 69(11): 7025-7048, 202
Externí odkaz:
http://arxiv.org/abs/2411.14087
Finding a mass formula for a given class of linear codes is a fundamental problem in combinatorics and coding theory. In this paper, we consider the action of the unitary (resp. symplectic) group on the set of all Hermitian (resp. symplectic) linear
Externí odkaz:
http://arxiv.org/abs/2410.13578
We introduce the notion of logarithmically concave (or log-concave) sequences in Coding Theory. A sequence $a_0, a_1, \dots, a_n$ of real numbers is called log-concave if $a_i^2 \ge a_{i-1}a_{i+1}$ for all $1 \le i \le n-1$. A natural sequence of pos
Externí odkaz:
http://arxiv.org/abs/2410.04412
Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes. Nevertheless, there
Externí odkaz:
http://arxiv.org/abs/2409.00404
Publikováno v:
Quantum Inf Process 23, 280 (2024)
Triorthogonal matrices were introduced in Quantum Information Theory in connection with distillation of magic states (Bravyi and Haah (2012)). We give an algorithm to construct binary triorthogonal matrices from binary self-dual codes. Further, we ge
Externí odkaz:
http://arxiv.org/abs/2408.09685
We define a triangle design as a partition of the set of $2$-dimensional subspaces of an $n$-dimensional vector space into triangles, where a triangle consists of three subspaces with the trivial, $0$-dimensional, intersection and $1$-dimensional mut
Externí odkaz:
http://arxiv.org/abs/2407.19157
We construct a ternary [49,25,7] code from the row span of a Jacobsthal matrix. It is equivalent to a Generalized Quadratic Residue (GQR) code in the sense of van Lint and MacWilliams (1978). These codes are the abelian generalizations of the quadrat
Externí odkaz:
http://arxiv.org/abs/2407.16310
The size of the Hamming distance spectrum of a code has received great attention in recent research. The main objective of this paper is to extend these significant theories to the $b$-symbol distance spectrum. We examine this question for various ty
Externí odkaz:
http://arxiv.org/abs/2404.02471
The existence of $q$-ary linear complementary pairs (LCPs) of codes with $q> 2$ has been completely characterized so far. This paper gives a characterization for the existence of binary LCPs of codes. As a result, we solve an open problem proposed by
Externí odkaz:
http://arxiv.org/abs/2312.09482
We explore a notion of bent sequence attached to the data consisting of an Hadamard matrix of order $n$ defined over the complex $q^{th}$ roots of unity, an eigenvalue of that matrix, and a Galois automorphism from the cyclotomic field of order $q.$
Externí odkaz:
http://arxiv.org/abs/2311.00354