Selfdual $\mathbb{F}_q$linear $\mathbb{F}_{q^t}$codes with an automorphism of prime order
W. Cary Huffman  Department of Mathematics and Statistics, Loyola University, Chicago, IL 60660, United States (email) Abstract: Additive codes over $\mathbb{F}_4$ are connected to binary quantum codes in [9]. As a natural generalization, nonbinary quantum codes in characteristic $p$ are connected to codes over $\mathbb{F}_{p^2}$ that are $\mathbb{F}_p$linear in [30]. These codes that arise as connections with quantum codes are selforthogonal under a particular inner product. We study a further generalization to codes termed $\mathbb{F}_q$linear $\mathbb{F}_{q^t}$codes. On these codes two different inner products are placed, one of which is the natural generalization of the inner products used in [9, 30]. We consider codes that are selfdual under one of these inner products and possess an automorphism of prime order. As an application of the theory developed, we classify some of these codes in the case $q=3$ and $t=2$.
Keywords: Additive codes, selfdual codes, code automorphisms.
Received: June 2012; Revised: August 2012; Available Online: January 2013. 
2016 Impact Factor.8
