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Nonbinary double-error-correcting codes designed by means of algebraic varieties

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1 Author(s)
Dumer, I. ; Inst. for Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia

Linear q-ary codes of growing length n→∞ and designed distance δ are studied. At first, we examine cyclic codes defined by the sets of code zeros {gi|i=qs+1, qs+1 +1, ···, qs+δ-2+1} over a primitive element g of GF(qm). Then special cubic varieties are designed and employed in order to attain distances δ=5, 6. The resulting double-error-correcting codes of length n=qm have r⩽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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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 6 )