Nonexistence Theorems for Perfect Codes over Finite Fields
(2012) In Bachelor's Theses in Mathematical Sciences MATX01 20121Mathematics (Faculty of Sciences)
- Abstract
- In this survey, we consider the trivial perfect codes which are the binary repetition codes of odd length and all codes that only contain one code word. We also take into acount, the Hamming codes as well as the two perfect Golay codes. We then prove that there do not exist any perfect codes over finite fields others than the ones above, using Lloyd's theorem.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/4358043
- author
- Jönsson, André LU
- supervisor
- organization
- course
- MATX01 20121
- year
- 2012
- type
- M2 - Bachelor Degree
- subject
- keywords
- perfect codes mathematics
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4017-2012
- ISSN
- 1654-6229
- other publication id
- 2012:K5
- language
- English
- id
- 4358043
- date added to LUP
- 2014-03-14 17:20:53
- date last changed
- 2014-03-14 17:20:53
@misc{4358043, abstract = {{In this survey, we consider the trivial perfect codes which are the binary repetition codes of odd length and all codes that only contain one code word. We also take into acount, the Hamming codes as well as the two perfect Golay codes. We then prove that there do not exist any perfect codes over finite fields others than the ones above, using Lloyd's theorem.}}, author = {{Jönsson, André}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Nonexistence Theorems for Perfect Codes over Finite Fields}}, year = {{2012}}, }