By P. G. Farrell (auth.), G. Longo (eds.)
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Additional resources for Algebraic Coding Theory and Applications
Vi vor sequences need to be stored, thus reducing the amo~t of storage required.
And canbination, a rOIl interdlange can be Il'ade so (colurm interdlange is not possible, as this destroys the cyclic properties of the cOOe). [H] can be found fran [GJ in the usual way. = x3 + x + 1 which belongs to 7. G. ------ l+x+x +x Hence [H] a 4 4 [1110 = 011 1 o I O! 110 1 00 lj H(x) lool I In this case there are four sets of cycliC translates. 'l'his is a single- error-correcting (SOC) cede. The rCMS of [GJ are multiples of G(x), so that all the code YJOrds of a cyclic code are multiples ot G(x).
Jest score The correct sequence is easily determined. G. ~R CASE Transmi tted sequence 11 01 11 10 10 Error " 00 10 00 00 00 Received " 11 11 11 10 10 ~ 11 12. t 1 G v.......... 1 . 1 '. C ~- ~ i .... ~ 1 '. c- - - ~. L. ; 1 7: t 1 ~-... t r. ' 11 Ie. i 1. 2 L Again, upper path selected when scores agree. B. --"OPC sec; . Again, the correct sequence can be selected, even at the third step. -vi vor sequences need to be stored, thus reducing the amo~t of storage required.