线性拟等重码的结构分析

Structure Analysis of Linear Quasi-Constant Weight Codes

Ｃ为二元正则［ｎ，ｋ，ｄ］线性拟等重码，我们证明：（１）如果ｎ＝２ｄ，则Ｃ等价于１阶Ｒｅｅｄ－Ｍｕｌｌｅｒ码ＲＭ（ｋ—１，１）；（２）如果ｎ≠２ｄ，且２ｋ－１－１为素数，则Ｃ等价于ＲＭ（ｋ－１，１）删除第１个分量后得到的线性码ＲＭ＊（ｋ—１，１）．另外，利用编码理论中著名的ＭａｃＷｉｌｌｉａｍｓ恒等式给出文［１］定理１的一个新的简洁证明．

C is a binary regular [n,k,d ] linear quasi-constant weight code. We show that(1)if n=2d,then C is equivalent to the first order Reed-Muller code RM (k - 1, 1 ), (2)if n≠2d, and2k-1 - 1 is a prime number,then C is equivalent to the punctured Reed-Muller code RM* (k-1, 1 )(deleting the first coordinate of RM (k - 1, 1 ) ). Furthermore, we present a new simple proof for Theorem 1 in[1] by using the well known MacWilliams identity in coding theory.