**Concatenated codes**

This article welcomes suggestions and amendments from others since the author of this article just presents what he thinks is right, and he might be wrong.

Fix *n*. We will use a binary symmetric channel *n* times to transmit *n* bits.

Firstly, choose a GV code with parameters over the finite field GF(2) for the inner code. There are bits of messages in the GV code.

Secondly, choose a Reed-Solomon code with parameters over the finite field for the outer code.

By choosing the above parameters, we can transmit symbols over the finite field for the overall code.

The encoding and decoding procedures are done as follows.

The source chooses symbols over the finite field to transmit. Encode the symbols using the Reed-Solomon code to obtain a codeword of length over the finite field . Then, for each symbol in sequence of the Reed-Solomon code, convert it into a -bit sequence and encode the resulting bit sequence using the GV code. Since the length of each bit sequence generated by the GV code is , the total length of the overall sequence is *n*.

The decoder will first decode each chunk, which is encoded by GV code, to obtain symbols over the finite field . After that, the decoder will use the Reed-solomon code to try to recover the symbols.

The choice of d and will determine the performance of the overall code against errors induced by the channel. More specifically, d and will determine the minimum Hamming distance of the overall code.

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