On contracted codes: an extension of Pless' theorem on codes

An analogue of the Pless symmetry codes

A series of monomial representations of SL2(p) is used to construct a new series of self-dual ternary codes of length 2(p + 1) for all primes p ≡ 5 (mod 8). In particular we find a new extremal self-dual ternary code of length 60.

An efficient secure channel coding scheme based on polar codes

In this paper, we propose a new framework for joint encryption encoding scheme based on polar codes, namely efficient and secure joint secret key encryption channel coding scheme. The issue of using new coding structure, i.e. polar codes in Rao-Nam (RN) like schemes is addressed. Cryptanalysis methods show that the proposed scheme has an acceptable level of security with a relatively smaller ke...

Linear codes on posets with extension property

We investigate linear and additive codes in partially ordered Hamming-like spaces that satisfy the extension property, meaning that automorphisms of ideals extend to automorphisms of the poset. The codes are naturally described in terms of translation association schemes that originate from the groups of linear isometries of the space. We address questions of duality and invariants of codes, es...

Gleason's theorem on self-dual codes

On McMillan's theorem about uniquely decipherable codes

Let len : A −→ N be the length function on the free monoid of all strings over a given non-empty finite set A. Let con : A −→ A be the concatenation map which to every string of strings associates their concatenation. A uniquely decipherable code is a finite set C ⊆ A such that con is injective on the submonoid C of A. This submonoid is then isomorphic to the submonoid C = con[C] of A freely ge...