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Construction of isodual codes from polycirculant matrices
- Publication Year :
- 2018
-
Abstract
- Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over $ \F_2$ in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over $\F_2,$ we show that binary double polycirculant codes are asymptotically good.
- Subjects :
- Computer Science - Cryptography and Security
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1811.03789
- Document Type :
- Working Paper