Abstract
We find the minimum distances of the binary <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(113, 57)</tex> , and ternary <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(37, 19), (61, 31), (71, 36)</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(73, 37)</tex> quadratic residue codes and the corresponding extended codes. These distances are <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15, 10, 11, 17</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</tex> , respectively, for the nonextended codes and are increased by one for the respective extended codes. We also characterize the minimum weight codewords for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(113, 57)</tex> binary code and its extended counterpart.
Keywords
Binary numberQuadratic equationTernary operationCode (set theory)Computer scienceCombinatoricsDiscrete mathematicsMathematicsAlgorithmArithmeticProgramming language
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Publication Info
- Year
- 1984
- Type
- article
- Volume
- 30
- Issue
- 2
- Pages
- 407-411
- Citations
- 32
- Access
- Closed
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Cite This
Don Coppersmith,
G. Seroussi
(1984).
On the minimum distance of some quadratic residue codes (Corresp.).
IEEE Transactions on Information Theory
, 30
(2)
, 407-411.
https://doi.org/10.1109/tit.1984.1056861
Identifiers
- DOI
- 10.1109/tit.1984.1056861