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FEW-WEIGHT CODES FROM TRACE CODES OVER
$R_{k}$
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 1 / August 2018
- Published online by Cambridge University Press:
- 03 May 2018, pp. 167-174
- Print publication:
- August 2018
-
- Article
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- You have access
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We construct two families of few-weight codes for the Lee weight over the ring
$R_{k}$
based on two different defining sets. For the first defining set, taking the Gray map, we obtain an infinite family of binary two-weight codes which are in fact
$2^{k}$
-fold replicated MacDonald codes. For the second defining set, we obtain two infinite families of few-weight codes. These few-weight codes can be used to implement secret-sharing schemes.
ON DEFINING SETS IN LATIN SQUARES AND TWO INTERSECTION PROBLEMS, ONE FOR LATIN SQUARES AND ONE FOR STEINER TRIPLE SYSTEMS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 82 / Issue 2 / October 2010
- Published online by Cambridge University Press:
- 16 August 2010, pp. 351-352
- Print publication:
- October 2010
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- Article
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