Complementary information set codes over GF(p)

Complementary information set codes (CIS codes) over a finite field GF ( p ) are closely connected to correlation-immune functions over GF ( p ), which are important cryptographic functions, where p is an odd prime. Using our CIS codes over GF ( p ) of minimum weight d + 1 , we can obtain p -ary cor...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2016-12, Vol.81 (3), p.541-555
Main Authors: Kim, Hyun Jin, Lee, Yoonjin
Format: Article
Language:English
Subjects:
Binary system
Circuits
Classification
Codes
Coding and Information Theory
Computer Science
Construction methods
Criteria
Cryptography
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Minimum weight
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Summary:Complementary information set codes (CIS codes) over a finite field GF ( p ) are closely connected to correlation-immune functions over GF ( p ), which are important cryptographic functions, where p is an odd prime. Using our CIS codes over GF ( p ) of minimum weight d + 1 , we can obtain p -ary correlation-immune function of strength d . We find an efficient method for constructing CIS codes over GF ( p ). We also find a criterion for checking equivalence of CIS codes over GF ( p ). We complete the classification of all inequivalent CIS codes over GF ( p ) of lengths up to 8 for p = 3 , 5 , 7 using our construction and criterion. We also find their weight enumerators and the order of their automorphism groups. The class of CIS codes over GF ( p ) includes self-dual codes over GF ( p ) as its subclass, and some CIS codes are formally self-dual codes as well; we sort out our classification results. Furthermore, we show that long CIS codes over GF ( p ) meet the Gilbert–Vashamov bound.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-015-0174-3