Abstract
We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F+2 + uF2 + vF2 + uvF2 of length 6 and size 212.Writing a typical generating matrix of the form [I3|A], with A being a 3×3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the generating matrices of self-dual codes of length 6. Using some special properties of elements of R, we end up with a family of generating matrices all of which give us the extended binary Golay code. We also prove the minimum distance property analytically.
Original language | English (US) |
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Pages (from-to) | 69-72 |
Number of pages | 4 |
Journal | Applied Mathematics and Information Sciences |
Volume | 8 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2014 |
Externally published | Yes |
Keywords
- Codes over rings
- Extended binary Golay code
- Extremal codes
- Gray map
- Lee weight
- Self-dual codes
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics