Linear transformations on codes

On One-Sided Ideals of Rings of Linear Transformations

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

Constructing network codes using Möbius transformations

We study error correcting constant dimension subspace codes for network coding. The codewords are F2-subspaces of F2n , having at most 1-dimensional intersections. F2n is contained in the automorphism group of the code. We give a lower bound for the size of such codes, being constructed by a greedy method. Further we describe a code in F22m with 23m codewords, for which we finally present a con...

Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes

Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...

Constacyclic Codes over Group Ring (Zq[v])/G

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...