Today we will discuss ways of converting GRS and RS codes into binary codes that can be implemented practically in real-world contexts. We will do this in two ways: with concatenated codes where we turn the GRS/RS codewords into bit strings and then apply a second layer of coding, and with BCH codes, where we take only those codewords that happen to have entries in the base field.
Before our class meeting, you should use the resources below to be able to learn the following. You should be reasonably fluent with these; we’ll answer some questions on them in class but not reteach them in detail.
Describe the idea of the concatenated code construction. Given two compatible codes, determine the length, dimension, and lower bound on the distance of the resulting concatenated code.
