Introduction to generalized hamming weight

Document Type : Promotional Paper

Author

Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran

Abstract

Let $C$ be a code over a finite field. The r-th Generalized Hamming weight(GHW), denoted by $d_r(C)$, is defined the minimum of support sizes of r- dimensional subcodes of
$C$.GHW is important for its application in several fields such as Cryptography, Electronic Engineering, Computer and telecommunication Engineering. In this work, we will investigate this conception and its application.

Keywords

References

[1] S. T. Dougherty and S. Han, Higher Weights and Generalized MDS Codes, Korean Math. Soc., no. 6 (2010) 1167–1182.
[2] F. Farhang Baftani and H. R. Maimani, The weight Hierarchy of Hadamard Codes, Facta Univ. Ser. Math. Inform., 34 (2019) 797–803.
[3] F. Farhang Baftani and H. R. Maimani, The weight Hierarchy of Ham (r,q), Italian Journal of Pure and applied Mathematics, no 45, (2021).
[4] F. Farhang Baftani, The weight Hierarchy of(u, u+v) Construction of Codes, The 51st Annual Iranian Mathematics Conference, Kashan, Iran, (2021) 15–20.
[5] F. Farhang Baftani, The weight Hierarchy of some BCH Codes, 11th International Conference on Graph Theory and Algebraic Combinatorics, Urmia University, Urmia, Iran, (2021).
[6] R. G. Gallager, Information Theory and Reliable Communication, Willey, New York, 1968.
[7] S. Ling and C. Xing, Coding Theory A First Course, Cambridge university press, 2004.
[8] L. H. Ozarow and A. D. Wyner, Wire- tap channel 2, AT T Bell Labs Tech. J., 63 (1984) 2135-2157.
[9] V. K. Wei, Generalized Hamming Weights for linear codes, IEEE Trans. Inform. Theory, 37 (1991) 1412–1418. 

Files

History

  • Receive Date: 07 October 2021
  • Revise Date: 03 January 2022
  • Accept Date: 13 February 2022
  • Publish Date: 23 August 2021

Share

How to cite

Statistics