4 papers
Moment-based linear programming bounds for locally recoverable codes
Shujian Li, Hengjia Wei, Maosheng Xiong
In this paper we derive new Delsarte-type linear programming bounds for -ary -locally recoverable codes (LRCs) with three attributes: first, the variable set is comparabl…
Counterexamples to Charpin's Conjecture on BCH codes
Run Zheng, Yaoran Yang, Yutong Zhang +1
Determining the exact minimum distance of BCH codes is a longstanding and challenging problem. In this paper, we construct an infinite family of primitive narrow-sense BCH codes wh…
On generalized covering radii of binary primitive double-error-correcting BCH codes
Maosheng Xiong, Chi Hoi Yip
The generalized covering radii (GCR) of linear codes are a fundamental higher-dimensional extension of the classical covering radius. While the second and third GCR of binary primi…
On covering radius of generalized Zetterberg codes
Haode Yan, Maosheng Xiong
We employ analytic number theoretic techniques, specifically character sums and Weil type estimates, to study the covering radius of the generalized Zetterberg codes over all finit…