Adding Two Information Symbols to Certain Nonbinary BCH Codes and Some Applications

This paper is a compendium of results based upon a simple observation: two information symbols can be appended to the code words of certain BCH codes without weakening the error correction capability of these codes. We define a class of BCH codes called "maximally redundant codes" in Section I I ; for codes in this class a simple method is given for appending two columns to the check matrix which does not increase the number of check symbols for the code nor decrease the error correction capability of these codes. Section I I I gives the parameters for lengthened Reed-Solomon codes and shows that such codes are perfect for single error correction. Section IV discusses a general decoding algorithm for the lengthened codes and shows that these codes are invariant under certain permutation operations. Section V discusses a method for constructing the lengthened codes from cosets of the original code. We use this approach in Section VI to determine the lower bounds on the number of high weight cosets 2405