Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $q$ be a power of prime number $p$ and let $F_{q^2}$ be a finite field of order $q^2$. Suppose that "-" be a conjugation operation that is defined as follow:

$-:F_{q^2} ‎\longrightarrow‎ ‎F_{q^2}$

$x ‎\longmapsto‎ x^q$

Let $C$ be a cyclic code of length n over $F_{q^2}$ with the generator polynomial $g(x)$ and let $\bar{C}=\lbrace \bar{c} : c \in C \rbrace$ be the conjugate code of $C$.

It is obvious that $\bar{C}$ is also a cyclic code.

Is it possible to determine the generator polynomial of $\bar{C}$ from $g(x)$?

share|improve this question
2  
The obvious choice works. –  Felipe Voloch Dec 16 '11 at 18:33
    
Thank you for your helpful answer. –  Zahra Dec 17 '11 at 19:20
add comment

1 Answer

up vote 2 down vote accepted

The generator polynomial of $\bar{C}$ is $‎\overline{g(x)}‎$. Because the conjugation operation is distributive over summation and multiplication.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.