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Complementary information set codes over GF(p)

Title
Complementary information set codes over GF(p)
Authors
Kim H.J.Lee Y.
Ewha Authors
이윤진김현진
SCOPUS Author ID
이윤진scopus; 김현진scopus
Issue Date
2016
Journal Title
Designs, Codes, and Cryptography
ISSN
0925-1022JCR Link
Citation
vol. 81, no. 3, pp. 541 - 555
Keywords
CodeComplementary information set codeCorrelation immuneEquivalenceGilbert–Vashamov boundSelf-dual code
Publisher
Springer New York LLC
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
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. © 2016, Springer Science+Business Media New York.
DOI
10.1007/s10623-015-0174-3
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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