On the existence of quaternary Hermitian LCD codes with Hermitian dual distance 1

04/15/2021
by   Keita Ishizuka, et al.
0

For k ≥ 2 and a positive integer d_0, we show that if there exists no quaternary Hermitian linear complementary dual [n,k,d] code with d ≥ d_0 and Hermitian dual distance greater than or equal to 2, then there exists no quaternary Hermitian linear complementary dual [n,k,d] code with d ≥ d_0 and Hermitian dual distance 1. As a consequence, we generalize a result by Araya, Harada and Saito on the nonexistence of some quaternary Hermitian linear complementary dual codes.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/23/2019

Remark on subcodes of linear complementary dual codes

We show that any ternary Euclidean (resp. quaternary Hermitian) linear c...
03/30/2018

On the classification of linear complementary dual codes

We give a complete classification of binary linear complementary dual co...
04/16/2019

Quaternary Hermitian linear complementary dual codes

The largest minimum weights among quaternary Hermitian linear complement...
03/23/2022

An introduction to using dual quaternions to study kinematics

We advocate for the use of dual quaternions to represent poses, twists, ...
02/06/2022

Galois LCD codes over mixed alphabets

We study (Galois) linear complementary dual codes over mixed alphabets a...
08/23/2019

On the minimum weights of ternary linear complementary dual codes

It is a fundamental problem to determine the largest minimum weight d_3(...
04/02/2020

Gopala-Hemachandra codes revisited

Gopala-Hemachandra codes are a variation of the Fibonacci universal code...