منابع مشابه
Checkable Codes from Group Rings
Abstract—We study codes with a single check element derived from group rings, namely, checkable codes. The notion of a codecheckable group ring is introduced. Necessary and sufficient conditions for a group ring to be code-checkable are given in the case where the group is a finite abelian group and the ring is a finite field. This characterization leads to many good examples, among which two c...
متن کاملDouble circulant self-dual and LCD codes over Galois rings
This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic p and order p with p and odd prime. When p ≡ 3 (mod 4), we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to Z p2 . Using random coding, we obtain families of asymptotically good self-dual an...
متن کاملCodes from zero-divisors and units in group rings
We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in idea...
متن کاملConvolutional codes from units in matrix and group rings
A general method for constructing convolutional codes from units in Laurent series over matrix rings is presented. Using group rings as matrix rings, this forms a basis for in-depth exploration of convolutional codes from group ring encodings, wherein the ring in the group ring is itself a group ring. The method is used to algebraically construct series of convolutional codes. Algebraic methods...
متن کاملOn {\sigma}-LCD codes
Linear complementary pairs (LCP) of codes play an important role in armoring implementations against side-channel attacks and fault injection attacks. One of the most common ways to construct LCP of codes is to use Euclidean linear complementary dual (LCD) codes. In this paper, we first introduce the concept of linear codes with σ complementary dual (σ-LCD), which includes known Euclidean LCD c...
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ژورنال
عنوان ژورنال: Sakarya University Journal of Science
سال: 2019
ISSN: 1301-4048
DOI: 10.16984/saufenbilder.459123