On the Distribution of p-Error Linear Complexity of p-Ary Sequences with Period pn

Miao TANG  Juxiang WANG  Minjia SHI  Jing LIANG  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E102-D   No.12   pp.2595-2598
Publication Date: 2019/12/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2019EDL8093
Type of Manuscript: LETTER
Category: Fundamentals of Information Systems
Keyword: 
periodic sequence,  k-error linear complexity,  counting function,  stream ciphers,  

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Summary: 
Linear complexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-error linear complexity of p-ary sequences with period pn. For p-ary sequences of period pn with linear complexity pn-p+1, n≥1, we present all possible values of the p-error linear complexity, and derive the exact formulas to count the number of the sequences with any given p-error linear complexity.