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Nonbinary random error-correcting codes (Corresp.)

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Primitive BCH codes with symbols from GF(q) and designed distance d have parameter values begin{align} text{block length} &= n = q^m - 1 \ text{check symbols/block} &= r leq m(d - 1) end{align} where m is any positive integer. For many nonbinary BCH codes (called maximally redundant codes), the maximum number of check symbols per block is required, i.e. r = m(d - 1) . Conditions whereby a primitive nonbinary BCH code is maximally redundant are discussed. It is shown that a class of codes exists, with symbols from GF(q) , based upon doubly lengthened Reed-Solomon codes over GF(q^m) , having parameter values begin{align} text{block length} &= n = m(q^m + 1) \ text{check symbols/block} &= r = m(d - 1) \ text{designed distance} &= d end{align} where again m is any positive integer. Thus this class of codes extends the block length of maximally redundant codes by a multiplicative factor exceeding m , while retaining the same designed distance and same number of check symbols.

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IEEE Transactions on Information Theory  (Volume:16 ,  Issue: 2 )