»ã±¨±êÌâ (Title)£ºÏßÐÔ²åÈëɾ³ýÂëµÄµÄÈô¸É½çºÍ×îÓÅÂëµÄ»ú¹Ø£¨Strict Half-Singleton Bound, Strict Direct Upper Bound for Linear Insertion-Deletion Codes and Optimal Codes£©

»ã±¨ÈË (Speaker)£º Ö£´ó±ò ½ÌÊÚ£¨ºþ±±´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê4ÔÂ14ÈÕ(ÖÜÎå) 09£º30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÕźìÁ« ½ÌÊÚ

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»ã±¨ÌáÒª£ºLet C be an [n, k] linear code over the finite field F_q. Let d_I(C) denote its insertion-deletion (insdel for short) distance, which characterizes the insdel error-correcting capability of C. In this paper we propose a strict half-Singleton upper bound d_I(\C) ¡Ü2(n-2k+1)if C does not contain the codeword with all 1s, which generalizes the half-Singleton bound on the insdel distances of linear codes due to Cheng-Guruswami-Haeupler-Li, and a stronger direct upper bound d_I(C)¡Ü2(d_H(C)-t) under a weak condition, where t¡Ý1 is a positive integer determined by the generator matrix and d_H(C) denotes the Hamming distance of C. A sufficient condition for a linear code attaining the strict half-Singleton bound is given. We prove that the code length of an optimal binary linear insdel code w.r.t. the (strict) half- Singleton bound is about twice its dimension and conjecture that optimal binary linear insdel codes have exact parameters [2k, k, 4] or [2k+1, k, 4] w.r.t. the half- or strict half-Singleton bound, respectively.