1
$\begingroup$

This is for my understanding. What am I missing?

$\endgroup$
2
$\begingroup$

Suppose we consider $s$-folded Reed-Solomon codes that are based on polynomials over a field $\mathbb{F} = \mathrm{GF}(p^t)$. Then the alphabet of those codes is of size $p^{t \cdot s}$. Hence, in order to be linear, those codes should be closed under multiplication by scalar from the field $\mathbb{F}' = \mathrm{GF}(p^{t \cdot s})$. There is no apparent reason why they should be closed under such operation.

However, it is true that they are closed under multiplication by scalar from $\mathbb{F}$. In other words, the codes are $\mathbb{F}$-linear.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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