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Complementary information set codes over GF(p)
- Complementary information set codes over GF(p)
- Kim H.J.; Lee Y.
- Ewha Authors
- 이윤진; 김현진
- SCOPUS Author ID
- 이윤진; 김현진
- Issue Date
- Journal Title
- Designs, Codes, and Cryptography
- vol. 81, no. 3, pp. 541 - 555
- Code; Complementary information set code; Correlation immune; Equivalence; Gilbert–Vashamov bound; Self-dual code
- Springer New York LLC
- SCI; SCIE; SCOPUS
- 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. Â© 2016, Springer Science+Business Media New York.
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