ISSN:
1573-7586
Keywords:
Error-correcting codes
;
fundamental
;
parameters
;
completely regular codes
;
Hamming graph
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract A code C⊑ F n is s-regular provided, forevery vertex x ∈ F n, if x is atdistance at most s from C then thenumber of codewords y ∈ C at distance ifrom x depends only on i and the distancefrom x to C. If ρ denotesthe covering radius of C and C is ρ-regular,then C is said to be completely regular. SupposeC is a code with minimum distance d,strength t as an orthogonal array, and dual degrees *. We prove that d ≤ 2t + 1 whenC is completely regular (with the exception of binaryrepetition codes). The same bound holds when C is(t + 1)-regular. For unrestricted codes, we show thatd ≤ s * + t unless C is a binary repetitioncode.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008395813214
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