4 papers · 1 filter
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…
Exact Minimum Distance of the Ding--Li--Xia Cyclic Codes
Yutong Zhang, Yaoran Yang
The cyclic codes introduced by Ding, Li, and Xia form a nonbinary generalization of punctured binary Reed--Muller codes. Ding, Li, and Xia established the bounds $(q^…
Algebraic Resolutions of Seven Open Problems on Cyclic and Negacyclic Codes Supporting Designs
Yutong Zhang, Yaoran Yang
This paper gives a unified algebraic solution to seven open problems of Wang, Tang and Ding on cyclic, negacyclic and constacyclic codes supporting designs. For the cyclic code \[…
Intermediate Constacyclic Codes and Scalar-Residue Reed--Muller Layers
Yaoran Yang, Yutong Zhang
A 2024 paper of Sun, Ding and Wang introduced a second class of constacyclic codes over finite fields, denoted , with length , where and the…