A relationship between linear complexity and kapa-error linear complexity

Linear complexity is an important cryptographic criterion of stream ciphers. The k-error linear complexity of a periodic sequence of period N is defined as the smallest linear complexity that can be obtained by changing k or fewer bits of the sequence per period. This article shows a relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.

[1]  Peter Elias,et al.  Universal codeword sets and representations of the integers , 1975, IEEE Trans. Inf. Theory.

[2]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[3]  Cunsheng Ding,et al.  The Stability Theory of Stream Ciphers , 1991, Lecture Notes in Computer Science.

[4]  Daniel J. Costello,et al.  Polynomial weights and code constructions , 1973, IEEE Trans. Inf. Theory.

[5]  Rudolf Ahlswede,et al.  Universal coding of integers and unbounded search trees , 1997, IEEE Trans. Inf. Theory.

[6]  Mark Stamp,et al.  An algorithm for the k-error linear complexity of binary sequences with period 2n , 1993, IEEE Trans. Inf. Theory.

[7]  Andrew Chi-Chih Yao,et al.  An Almost Optimal Algorithm for Unbounded Searching , 1976, Inf. Process. Lett..

[8]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[9]  Ian H. Witten,et al.  Text Compression , 1990, 125 Problems in Text Algorithms.

[10]  Takashi Amemiya,et al.  A New Class of the Universal Representation for the Positive Integers , 1993 .

[11]  Quentin F. Stout.  Improved prefix encodings of the natural numbers (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[12]  Michael Rodeh,et al.  Economical encoding of commas between strings , 1978, CACM.