6 papers
Cyclic codes and cyclically covering subspaces
Xuan Wang, Minjia Shi
A subspace of is called cyclically covering if the union of can cover the whole space , where is the cyclic shift, $0 \leqslant i \leq…
On zero-sum polytopes: reciprocity, rigidity, and cyclic sieving
Dongchun Han, Xuan Wang, Hanbin Zhang +1
Let be a finite abelian group of order , and let denote the set of zero-sum sequences over of length . We introduce the zero-sum polytope $\mathcal P…
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…
Maximum Size -Intersecting Families and Anticodes
Xuan Wang, Tuvi Etzion, Denis Krotov +1
The maximum size of -intersecting families is one of the most celebrated topics in combinatorics, and its size is known as the Erdős-Ko-Rado theorem. Such intersecting families,…
Log-Concave Sequences in Coding Theory
Minjia Shi, Xuan Wang, Junmin An +1
We introduce the notion of logarithmically concave (or log-concave) sequences in Coding Theory. A sequence of real numbers is called log-concave if $a_i^2 \g…