Results 241 to 250 of about 1,011,482 (281)

Linear codes and the mitochondrial genetic code

Biosystems, 2019
The origin of the genetic code can certainly be regarded as one of the most challenging problems in the theory of molecular evolution. Thus the known variants of the genetic code and a possible common ancestry of them haven been studied extensively in the literature. Gonzalez et al.
Elena Fimmel, Lutz Strüngmann
openaire   +2 more sources

The category of linear codes

IEEE Transactions on Information Theory, 1998
Summary: Slepian (1960) introduced a structure theory for linear, binary codes and proved that every such code was uniquely the sum of indecomposable codes. He had hoped to produce a canonical form for the generator matrix of an indecomposable code so that he might read off the properties of the code from such a matrix, but such a program proved ...
openaire   +1 more source

Linearized Goppa Codes

2018 IEEE International Symposium on Information Theory (ISIT), 2018
In this paper, we construct a new family of codes-linearized Goppa codes embedded with Hamming and rank metric, and determine their parameters. In addition, we give a decoding method with respect to Hamming metric.
openaire   +1 more source

Linear codes and weights [PDF]

Australas. J Comb., 2020
We give an algebraic characterization of weight functions on linear codes, i.e. vector spaces of \(n\)-tuples over a finite field. Specifically, given a function from a finite vector space \(V\) to the nonnegative integers, we determine precisely when \(V\) can be replaced (isomorphically) by a space of \(n\)-tuples so that the given function becomes ...
openaire   +1 more source

A Propagation Rule for Linear Codes

Applicable Algebra in Engineering, Communication and Computing, 2000
By a propagation rule it is meant a procedure or a theorem leading to new codes from old ones. The authors introduce a propagation rule for linear codes by considering certain function field extensions. The parameters (length, dimension, distance) of the new code are related to the parameters of the old code and also to three chosen integers.
Harald Niederreiter, Chaoping Xing
openaire   +2 more sources

Extendability of Ternary Linear Codes

Designs, Codes and Cryptography, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

An Extension Theorem for Linear Codes

Designs, Codes and Cryptography, 1999
The author gives a simple sufficient condition for the existence of an extension of an \([n,k,d]_q\) code (with \((d,q)=1\)) to an \([n+1,k,d+1]_q\) code: if the weights of the code are all congruent to \(0\) or \(d\) modulo \(q\) then the code can be extended and the weights of the new code are all congruent to \(0\) or \(d+1\) modulo \(q\). The proof
openaire   +1 more source

Quaternary Linear Codes and Related Binary Subfield Codes

IEEE Transactions on Information Theory, 2022
Wu Yansheng, Chengju Li, Fu Xiao
exaly  

Linear $$\ell $$-intersection pairs of codes and their applications

Designs, Codes, and Cryptography, 2020
T Aaron Gulliver, Somphong Jitman
exaly  

Linear codes

1992
Abstract In this chapter we begin by taking another look at our example codes from Chapter 1 in the light of a natural arithmetic on B. That will lead us to define a special class of codes called linear codes (some authors call these group codes). Linear codes are amenable to the standard techniques of linear algebra and that makes it
openaire   +1 more source