6 papers
Generalized BCH Codes and Twisted Goppa Codes Attaining Their Designed Distances
Yaqi Chen, Hao Chen, Cunsheng Ding +3
Determining the true minimum distance of an alternant code remains a notoriously difficult problem in coding theory. In this paper, we study the minimum distances of generalized BC…
Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound
Xiaoqiang Wang, Xun Song, Dabin Zheng +2
In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root boun…
On the Minimum Distances of Some Families of Goppa Codes and BCH Codes
Yaqi Chen, Hao Chen, Cunsheng Ding +1
Goppa codes form an important class of alternant codes with wide applications in algebraic coding theory and code-based cryptography. Determining the true minimum distance of a Gop…
On the Minimum Distances of Some Families of BCH Codes
Yaqi Chen, Hao Chen, Cunsheng Ding +1
BCH codes form an important class of cyclic codes, which have applications in communication and data storage systems. Although the BCH bound provides a lower bound on the minimum d…
Infinitely many families of distance-optimal binary linear codes with respect to the sphere packing bound
Hao Chen, Conghui Xie, Cunsheng Ding
R. W. Hamming published the Hamming codes and the sphere packing bound in 1950. In the past 75 years, infinite families of distance-optimal linear codes over finite fields with min…
Some constructions of non-generalized Reed-Solomon MDS Codes
Kanat Abdukhalikov, Cunsheng Ding, Gyanendra K. Verma
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices fo…