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Nonexistence Theorems for Perfect Codes over Finite Fields

Jönsson, André LU (2012) In Bachelor's Theses in Mathematical Sciences MATX01 20121
Mathematics (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:
author
Jönsson, André LU
supervisor
organization
course
MATX01 20121
year
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},
  keyword      = {perfect codes mathematics},
  language     = {eng},
  note         = {Student Paper},
  series       = {Bachelor's Theses in Mathematical Sciences},
  title        = {Nonexistence Theorems for Perfect Codes over Finite Fields},
  year         = {2012},
}