Complementary information set codes over GF(p)

Hyun Jin Kim, Yoonjin Lee

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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.

Original languageEnglish
Pages (from-to)541-555
Number of pages15
JournalDesigns, Codes, and Cryptography
Volume81
Issue number3
DOIs
Publication statusPublished - 2016 Dec 1

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All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Applied Mathematics

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