»ã±¨±êÌâ (Title)£º´ïµ½Griesmer½çµÄ×îÓŶþÔª×ÔÕý½»ÂëµÄ×êÑУ¨Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances£©

»ã±¨ÈË (Speaker)£º Ê©Ãô¼Ó ½ÌÊÚ£¨°²»Õ´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê4ÔÂ14ÈÕ(ÖÜÎå) 10£º30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÕźìÁ«¡¢¶¡Ñó

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»ã±¨ÌáÒª£ºLet dso(n, k) denote the largest minimum distance among all binary self-orthogonal [n, k] codes. The determination of dso(n, k) has been a fundamental and difficult problem in coding theory because there are too many binary self-orthogonal codes as the dimension k increases. First, we develop a general method to determine the exact value of dso(n, k) for k= 5, 6 and show that the two conjectures made by Kim and Choi in (IEEE Trans. Inf. Theory 2022, 68(11): 7159-7164.) are true. Further, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some related residual codes. Using such a characterization, we determine the exact value of dso(n,7) except for five special cases. In addition, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code.