Patent ID: 8589364

Claim:
A computer-implemented method for systematic encoding of an information vector for use in correction of all asymmetric errors of maximum magnitude l and executed by a processor, comprising: a) providing a q-ary information vector having k information digits, (x k-1 ,x k-2 , . . . ,x 0 ); b) computing a, the value of (x k-1 ,x k-2 , . . . ,x 0 ) mod (l+1) as a vector over (l+1) according to the formula a=y k-1 ( l+ 1) k-1 +y k-2 ( l+ 1) k-2 +. . . +y 0 ( l+ 1) 0 , where y i = x i mod( l+ 1), iε{ 0,1, . . . , k− 1}; c) representing a in radix ⌈ q l + 1 ⌉ number with r digits: (a r-1 ,a r-2 , . . . ,a 0 ), where r ≥ k × log ⁡ ( l + 1 ) log ⁢ ⌈ q l + 1 ⌉ ; d) computing the check part, c, according to the formula c=(c r-1 ,c r-2 , . . . ,c 0 ), where c i =(l+1)a i ,∀iε{0,1, . . . , r−1}; and e) outputting an encoded vector that includes the information digits and check part, wherein any two check parts computed according to step (d) are at least l+1 apart.