報告題目：An improvement for error-correcting pairs of some special MDS codes

報告時間：2024年4月14日上午9:00-10:00

報告地點：kaiyun開云官方網(wǎng)站犀浦校區(qū)7教7504

報告人：廖群英

摘要：The error-correcting pair is a general algebraic decoding method for linear codes. Since every linear code is contained in an MDS linear code with the same minimum distance over some finite field extensions, we focus on MDS linear codes. Recently, He and Liao showed that for an MDS linear code C with minimum distance 2l+2, if it has an l-

error-correcting pair, then the parameters of the pair have three possibilities. Moreover, for the first case, they gave a necessary condition for an MDS linear code C with minimum distance 2l+2 to have an l-error-correcting pair, and for the other two cases, they only gave some counterexamples. For the second case, in this talk, we give a necessary condition for an MDS linear code C with minimum distance 2l+2 to have an l-error-correcting pair, and then basing on the Product Singleton Bound, we prove that there are two cases for such pairs, and then give some counterexamples basing on twisted generalized Reed-Solomon codes for these cases.

報告人簡介：廖群英，四川師范大學博士研究生導師、清華大學博士后、中國數(shù)學奧林匹克高級教練員，主要從事編碼和密碼的數(shù)學理論研究，曾參加國家自然科學基金重點項目一項，主持自然科學青年基金和面上項目、教育部博士點基金項目、四川省杰出青年學術技術帶頭人培育計劃項目、四川省科技廳應用基礎研究計劃重點項目，主研總參預研項目等；入選成都市優(yōu)秀女性人才信息庫，第十一批四川省學術技術帶頭人后備人選。

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