Linear complementary dual, maximum distance separable codes

01/14/2019
by   Ted Hurley, et al.
0

Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given n and r<n, with n or r (or both) odd, MDS LCD (n,r) codes are constructed over finite fields whose characteristic does not divide n. Series of LCD MDS codes are constructed to required rate and required error-correcting capability. Given the field GF(q) and n/(q-1), LCD MDS codes of length n and dimension r are explicitly constructed over GF(q) for all r<n when n is odd and for all odd r<n when n is even. Series of asymptotically good LCD MDS codes are explicitly constructed. Efficient encoding and decoding algorithms exist for all the constructed codes. Linear complementary dual codes have importance in data storage, communications' systems and security.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/18/2019

Maximum distance separable codes to order

Maximum distance separable (MDS) are constructed to required specificati...
research
09/14/2021

Linear block and convolutional MDS codes to required rate, distance and type

Algebraic methods for the design of series of maximum distance separable...
research
05/18/2021

New LCD MDS codes of non-Reed-Solomon type

Both linear complementary dual (LCD) codes and maximum distance separabl...
research
01/03/2018

On maximum distance separable group codes with complementary dual

Given an LCD group code C in a group algebra KG, we inspect kinship betw...
research
02/03/2018

Coding Theory: the unit-derived methodology

The unit-derived method in coding theory is shown to be a unique optimal...
research
01/03/2018

On maximum distance separable group codes with complementary duals

Given an LCD group code C in a group algebra KG, we inspect kinship betw...
research
05/14/2020

Minimizing the alphabet size of erasure codes with restricted decoding sets

A Maximum Distance Separable code over an alphabet F is defined via an e...

Please sign up or login with your details

Forgot password? Click here to reset