CAJ | 학술논문

对环 Zpl导出的多元Kerdock-code序列的部分周期性质进行了研究，这里 p为任意奇素数，l为任意正整数。利用特征为 pl的Galois环上不完全指数和的非平凡上界，对上述 p元Kerdock-code序列的非周期自相关性及互相关性进行了估计，同时对序列的部分周期分布和部分周期独立 r-样式分布也进行了刻画。结果表明，此类序列具有极低的非周期自相关性及互相关性，同时其部分周期分布和部分周期独立 r-样式分布也是渐进均匀的，在密码学和通信领域具有潜在的应用价值。
대배 Zpl도출적다원Kerdock-code서렬적부분주기성질진행료연구，저리 p위임의기소수，l위임의정정수。이용특정위 pl적Galois배상불완전지수화적비평범상계，대상술 p원Kerdock-code서렬적비주기자상관성급호상관성진행료고계，동시대서렬적부분주기분포화부분주기독립 r-양식분포야진행료각화。결과표명，차류서렬구유겁저적비주기자상관성급호상관성，동시기부분주기분포화부분주기독립 r-양식분포야시점진균균적，재밀마학화통신영역구유잠재적응용개치。
The partial period properties of the Kerdock-code sequences derived from Zpl are studied ,where p is an odd prime and l is an arbitrary positive integer .Utilizing a nontrivial upper bound for the incomplete exponential sums over Galois rings of characteristic pl ,we obtain the upper bounds for the aperiodic autocorrelation and crosscorrelation of the p-ary Kerdock-code se-quences derived from Zpl .Also we analyze the partial period distributions and the partial period independent r-pattern distributions of these sequences .The results show that such sequences have low aperiodic autocorrelation and crosscorrelation ,and their partial period distributions and partial period independent r-pattern distributions are asymptotically uniform ,which indicates that these se-quences have strong potential applications in communication systems and cryptography .