On Linear Complementary Pair of nD Cyclic Codes

Date

2018-12-01

Author

Guneri, Cem
Özkaya, Buket
Sayici, Selcen

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The security parameter for a linear complementary pair (C, D) of codes is defined to be the minimum of the minimum distances d(C) and d(D-perpendicular to). Recently, Carlet et al. showed that if C and D are both cyclic or both 2-D cyclic linear complementary pair of codes, and then, C and D-perpendicular to are equivalent codes. Hence, the security parameter for cyclic and 2-D cyclic linear complementary pair of codes is simply d(C). We extend this result to nD cyclic linear complementary pair of codes. The proof of Carlet et al. for the 2-D cyclic case is based on the trace representation of the codes, which is technical and nontrivial to generalize. Our proof for the generalization is based on the zero sets of the ideals corresponding to nD cyclic codes.

Subject Keywords

LCP of codes, nD cyclic codes, abelian codes, code equivalence

URI

https://hdl.handle.net/11511/103356

Journal

IEEE COMMUNICATIONS LETTERS

DOI

https://doi.org/10.1109/lcomm.2018.2872046

Collections

Graduate School of Applied Mathematics, Article

Citation Formats

C. Guneri, B. Özkaya, and S. Sayici, “On Linear Complementary Pair of nD Cyclic Codes,” IEEE COMMUNICATIONS LETTERS, vol. 22, no. 12, pp. 2404–2406, 2018, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/103356.