A NOTE ON k -GALOIS LCD CODES OVER THE RING
Rongsheng Wu, Minjia Shi · Bulletin of the Australian Mathematical Society · 2020
Abstract We study the k -Galois linear complementary dual (LCD) codes over the finite chain ring $R=\mathbb {F}_q+u\mathbb {F}_q$ with $u^2=0$ , where $q=p^e$ and p is a prime number. We give a sufficient condition on the generator matrix for the existence of k -Galois LCD codes over R . Finally, we show that a linear code over R (for $k=0, q> 3$ ) is equivalent to a Euclidean LCD code, and a linear code over R (for $0 , $(p^{e-k}+1)\mid (p^e-1)$ and ${(p^e-1)}/{(p^{e-k}+1)}>1$ ) is equivalent to a k -Galois LCD code.