关于λ-循环码λ-周期分布和广义λ-周期分布.pdf

摘要内容摘要:纠错码的周期分布成为编码理论的一个新的研究方向. 自1992年杨义先教授提出纠错码的周期分布后,国内许多学者对纠错码的周期分布问题展开探讨,,有利于非线性等重码和循环置换码的构造,,了解其内容结构特征有重要意义,,,证明了它们与Fq上坌q错码的周期分布和广义周期分布具有类似的性质,还分别找出了循环码和A一循环码具有入一周期的充要条件,并给出了有限域Fq上码长为礼((扎,q)=1),推广了文献中已有的关于R上纠错码周期分布和广义周期分布的一些结果. 关键词:x循环码,入周期分布,广义A一周期分布. Abstract Content:The period distributions oferror-correcting codes,in the classical coding theory,is anew investigation Yang Yi-xian proposed the period distribution oferror—correcting codes in 1992,many domestic scholars have probed the period distributions oferror-correcting codes,especially the period distributionsofcyclic period distribution of acyclic code isvaluable forthe con- tent ofthe cyclic on the period distributions ofcyclic codes must be propitious to know the structure ofcyclic codes,to construct nonlinear cyclic constant weight codes and cyclic trans— positional codesand to design signal with good —cyclic codes over thefinitefield日is thepromotion ofthe concept ofcyclic structures ofA—cyclic codes itisnecessary tostudy period structures of入一cyclic this pa- define the A—period distribution and the general入一period dis- tribution oferror-correcting codes over finitefieldR on thebasisof previous work,and show thatthey have some properties which are anal- ogous insome respects toproperties oftheperiod distribution and the general period distribution oferror-correcting isfound that the necessary and sufficientconditions which cyclic codes and入一 cyclic codes have入一period distribution also give the exact calculation formulas of入一period distribution and the smallest A-period distribution which入一cyclic codes have length n((n,q)=1) over日,and generalize theresults contained inthereferenc