Computer Science – Information Theory
Scientific paper
2009-12-30
Adv. Math. Commun. 5(2) 2011, 149-156
Computer Science
Information Theory
8 pages
Scientific paper
10.3934/amc.2011.5.149
The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.
Heden Olof
Krotov Denis
No associations
LandOfFree
On the structure of non-full-rank perfect codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the structure of non-full-rank perfect codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the structure of non-full-rank perfect codes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-103581