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Minimum distances of primitive narrow-sense BCH codes via good zero-sets
Run Zheng
Determining the exact minimum distances of BCH codes remains a open problem. We establish the minimum distances of several families of primitive narrow-sense BCH codes, showing tha…
Counterexamples to Charpin's Conjecture on BCH codes
Run Zheng, Yaoran Yang, Yutong Zhang +2
We construct an infinite family of -ary primitive narrow-sense BCH codes whose minimum distance strictly exceeds the Bose distance; in fact, the gap between the two can be arbit…
The dimension and Bose distance of some BCH codes of length
Run Zheng, Nung-Sing Sze, Zejun Huang
BCH codes are important error correction codes, widely utilized due to their robust algebraic structure, multi-error correcting capability, and efficient decoding algorithms. Despi…
The dimension and Bose distance of certain primitive BCH codes
Run Zheng, Nung-Sing Sze, Zejun Huang
BCH codes are a significant class of cyclic codes that play an important role in both theoretical research and practical applications. Their strong error-correcting abilities and e…