Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T15:29:36.807Z Has data issue: false hasContentIssue false
  • English
  • Français

NOTE ON SUPPORT WEIGHT DISTRIBUTION OF LINEAR CODES OVER $\mathbb{F}_{p}+u\mathbb{F}_{p}$

Part of: Theory of error-correcting codes and error-detecting codes

Published online by Cambridge University Press:  20 February 2015

JIAN GAO
JIAN GAO*
Affiliation:
Chern Institute of Mathematics and LPMC, Nankai University, China email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$, where $u^{2}=u$. A relation between the support weight distribution of a linear code $\mathscr{C}$ of type $p^{2k}$ over $R$ and its dual code $\mathscr{C}^{\bot }$ is established.

Keywords

finite nonchain ringsupport weightsupport weight distribution

MSC classification

Primary: 94B05: Linear codes, general
Secondary: 94B15: Cyclic codes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 345 - 350
Copyright
Copyright © 2015 Australian Mathematical Publishing Association Inc. 

References

Cui, J., ‘Support weight distribution of ℤ4-linear codes’, Discrete Math. 247 (2002), 135–145.Google Scholar
Cui, J. and Pei, J., ‘Generalized MacWilliams identities for ℤ4-linear codes’, IEEE Trans. Inform. Theory 50 (2004), 3302–3305.Google Scholar
Kaya, A., Yildiz, B. and Siap, I., ‘Quadratic residue codes over Fp+ vFpand their Gray images’, J. Pure Appl. Algebra 218 (2014), 1999–2011.Google Scholar
Kløve, T., ‘Support weight distribution of linear codes’, Discrete Math. 106 (1992), 311–316.Google Scholar
Simonis, J., ‘The effective length of subcodes’, Appl. Algebra Engrg. Comm. Comput. 5 (1992), 371–377.CrossRefGoogle Scholar
Wei, V. K., ‘Generalized Hamming weights for linear codes’, IEEE Trans. Inform. Theory 37 (1991), 1412–1418.Google Scholar
Zhu, S. and Wang, L., ‘A class of constacyclic codes over Fp+ vFpand its Gray image’, Discrete Math. 311 (2011), 2677–2682.Google Scholar
Zhu, S., Wang, Y. and Shi, M., ‘Some results on cyclic codes over F2+ vF2’, IEEE Trans. Inform. Theory 56 (2010), 1680–1684.Google Scholar