Abstract
Linear q-ary codes of growing length n/spl rarr//spl infin/ and designed distance /spl delta/ are studied. At first, we examine cyclic codes defined by the sets of code zeros {g/sup i/|i=q/sup s/+1, q/sup s+1/+1, /spl middot//spl middot//spl middot/, q/sup s+/spl delta/-2/+1} over a primitive element g of GF(q/sup m/). Then special cubic varieties are designed and employed in order to attain distances /spl delta/=5, 6. The resulting double-error-correcting codes of length n=q/sup m/ have r/spl les/2m+[m/3]+1 parity check symbols, and reduce the best known redundancy by [2m/3] symbols. A decoding procedure of complexity O(rn) operations is also considered.
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