DISTRIBUTION OF R-PATTERNS IN THE KERDOCK-CODE BINARY SEQUENCES AND THE HIGHEST LEVEL SEQUENCES OF PRIMITIVE SEQUENCES OVER $Z_{2^l}$

Honggang Hu; Dengguo Feng

Paper 2004/228 Original: eprint.iacr.org/2004/228 ↗

DISTRIBUTION OF R-PATTERNS IN THE KERDOCK-CODE BINARY SEQUENCES AND THE HIGHEST LEVEL SEQUENCES OF PRIMITIVE SEQUENCES OVER $Z_{2^l}$

Honggang Hu

Dengguo Feng

Abstract

The distribution of r-patterns is an important aspect of pseudorandomness for periodic sequences over finite field.The aim of this work is to study the distribution of r-patterns in the Kerdock-code binary sequences and the highest level sequences of primitive sequences over $Z_{2^l}$.By combining the local Weil bound with spectral analysis,we derive the upper bound of the deviation to uniform distribution.As a consequence,the recent result on the quantity is improved.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2004-09-09: last updated; 2004-09-09: published
Short URL: https://ia.cr/2004/228
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2004/228,
      author = {Honggang Hu and Dengguo Feng},
      title = {DISTRIBUTION OF R-PATTERNS IN THE KERDOCK-CODE BINARY SEQUENCES AND THE HIGHEST LEVEL SEQUENCES OF PRIMITIVE SEQUENCES OVER $Z_{2^l}$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/228},
      year = {2004},
      url = {https://eprint.iacr.org/2004/228}
}