10 papers
Multi-View Block Distance Distributions and Linear Programming Bounds for Locally Recoverable Codes with Availability
Ming-Hsuan Kang, Maosheng Xiong, Yu Hsuan Hsieh +1
We develop a multi-view linear-programming framework for locally recoverable codes with arbitrary fixed availability . For any retained order , the selected helpe…
Character sums on an oriented singer conic and explicit Ramanujan double covers
Pin-Chi Hung, Ming-Hsuan Kang
Let be odd. The trace conic in determines a Singer difference set in and a natural square-class lift to $\mat…
Linear Programming Bounds for Locally Recovery Codes II
Ming-Hsuan Kang, Maosheng Xiong
We give a polynomial-size linear programming bound for -ary all-symbol locally recoverable codes with locality parameters , without assuming linearity. The key idea is to…
Linear programming bounds for binary and ternary LCD Codes
Ming-Hsuan Kang, Maosheng Xiong
We derive linear programming (LP) bounds on the minimum distance of binary and ternary linear complementary dual (LCD) codes by imposing arithmetic constraints on their weight enum…
Information and Locality in Cayley Graphs
Ming-Hsuan Kang, Yu-Hsuan Hsieh
A de Bruijn sequence is the cyclic prototype of a Cayley-graph observation problem: when does the ordered label word on a translated window determine the vertex ? We distin…
Universal Cycles for Affine Planes and 3-Subspaces over Finite Fields
Yu Hsuan Hsieh, Ming-Hsuan Kang
We construct universal cycles for affine planes in for all prime powers and all , using sliding windows of length three. The construction is local-to-glo…
From Characters to Matrices: An Elementary Construction of Irreducible Representations of Finite Groups
Yu Hsuan Hsieh, Ming-Hsuan Kang
Let \(G\) be a finite group and let \(χ\) be an ordinary irreducible character. We give an elementary algorithm which constructs explicit matrices affording \(χ\). The regular repr…
Universal Cycles on Affine Lines
Ming-Hsuan Kang, Shin-Hsun Chou
A universal cycle is a cyclic sequence in which each object of a combinatorial family appears exactly once as a contiguous window. While such cycles are well understood for many di…
Algebraic Constructions of Universal Cycles on Grassmannians G_q(2,n)
Chen Yu Chi, Ming Hsuan Kang, Yu Hsuan Hsieh
We study universal cycles on the Grassmannian , the set of -dimensional -subspaces of . While their existence is known from inductive and…
De Bruijn Tori Without Zeros: A Field-Theoretic Perspective
Ming Hsuan Kang, Yu Hsuan Hsieh
We present an algebraic construction of trace-based De Bruijn tori over finite fields, focusing on the nonzero variant that omits the all-zero pattern. The construction arranges no…