码的弱等距
On weak isometries of Preparata codes
摘要：
设C1和C2是码距为d的码。码C1和C2称为弱等距码，如果存在映射J：C1->C2，使得对于C1的任意x，y，等式d（x，y）=d成立当且仅当d（J（x），J（y））=d。显然，两个码是弱等距的当且仅当这两个码的最小距离图是同构的。本文证明了长度n>=2^12的码是弱等距码当且仅当这些码是等价的。对于长度不小于2^10-1的删余码也得到了类似的结果。
英文摘要：
Let C1 and C2 be codes with code distance d. Codes C1 and C2 are called weakly isometric, if there exists a mapping J:C1->C2, such that for any x,y from C1 the equality d(x,y)=d holds if and only if d(J(x),J(y))=d. Obviously two codes are weakly isometric if and only if the minimal distance graphs of these codes are isomorphic. In this paper we prove that Preparata codes of length n>=2^12 are weakly isometric if and only if these codes are equivalent. The analogous result is obtained for punctured Preparata codes of length not less than 2^10-1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
