T. D. Duc

most citedNecessary Conditions for the Existence of Group-Invariant Butson Matrices and a New Family of Perfect Arrays

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math.CO2019★ 1 cited

Necessary Conditions for the Existence of Group-Invariant Butson Matrices and a New Family of Perfect Arrays

Tai Do Duc

Let $G$ be a finite abelian group and let $exp (G)$ denote the least common multiple of the orders of all elements of $G$ . A $B H (G, h)$ matrix is a $G$ -invariant $∣ G ∣ \times ∣ G ∣$ mat…

math.CO2019

Non-projective cyclic codes whose check polynomial contains two zeros

Tai Do Duc

Let $n \geq 3$ be a positive integer and let $F_{q^{k}}$ be the splitting field of $x^{n} - 1$ . By $γ$ we denote a primitive element of $F_{q^{k}}$ . Let $C$ be a cyclic co…

math.CO2019

Bilinear Forms on Finite Abelian Groups and Group-Invariant Butson Hadamard Matrices

Tai Do Duc, Bernhard Schmidt

Let $K$ be a finite abelian group and let $exp (K)$ denote the least common multiple of the orders of the elements of $K$ . A $B H (K, h)$ matrix is a $K$ -invariant $∣ K ∣ \times ∣ K ∣$ mat…

math.CO2019

New Constructions of Group-Invariant Butson Hadamard Matrices

Tai Do Duc

Let $G$ be a finite group and let $h$ be a positive integer. A $BH (G, h)$ matrix is a $G$ -invariant $∣ G ∣ \times ∣ G ∣$ matrix $H$ whose entries are complex $h$ th roots of unity…

math.CO2019

Unique Differences in Symmetric Subsets of $F_{p}$

Tai Do Duc, Bernhard Schmidt

Let $p$ be a prime and let $A$ be a subset of $F_{p}$ with $A = - A$ and $∣ A ∖ {0} ∣ \leq 2 lo g_{3} (p)$ . Then there is an element of $F_{p}$ which has a unique repr…

Necessary Conditions for the Existence of Group-Invariant Butson Matrices and a New Family of Perfect Arrays

Non-projective cyclic codes whose check polynomial contains two zeros

Bilinear Forms on Finite Abelian Groups and Group-Invariant Butson Hadamard Matrices

New Constructions of Group-Invariant Butson Hadamard Matrices

Unique Differences in Symmetric Subsets of Fp​

Unique Differences in Symmetric Subsets of $F_{p}$