6 papers
Double circulant LCD codes over and constructions for binary LCD codes
Xingxing Xu, Minjia Shi, Jon-Lark Kim
Linear complementary dual (LCD) codes are linear codes that intersect their dual trivially. We study double circulant (Euclidean) LCD codes over the finite chain ring $R=\mathbb F_…
New bounds for codes over Gaussian integers based on the Mannheim distance
Minjia Shi, Xuan Wang, Junmin An +1
We study linear codes over Gaussian integers equipped with the Mannheim distance. We develop Mannheim-metric analogues of several classical bounds. We derive an explicit formula fo…
Second order Recurrences, quadratic number fields and cyclic codes
Minjia Shi, Xuan Wang, Bouazzaoui Zakariae +2
Wall-Sun-Sun primes (shortly WSS primes) are defined as those primes such that the period of the Fibonacci recurrence is the same modulo and modulo This concept has…
Expanding self-orthogonal codes over a ring to self-dual codes and unimodular lattices
Minjia Shi, Sihui Tao, Jihoon Hong +1
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 e…
Triorthogonal Codes and Self-dual Codes
Minjia Shi, Haodong Lu, Jon-Lark Kim +1
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 bin…
A quaternary analogue of Tang-Ding codes
Minjia Shi, Sihui Tao, Jon-Lark Kim +1
In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves…