Relationship Between Weight Function and 1 – Norm

Authors

  • M Melna Frincy Department of Mathematics, Scott Christian College(Autonomous) Nagercoil- 629003, TamilNadu, India. Affiliated to Manonmanium Sundaranar University, Tirunelveli – 627012, Tamilnadu, India
  • J RobertVictor Edward Scott Christian College (Autonomous) Nagercoil 629003, TamilNadu, India Affiliated to Manonmanium Sundaranar University, Tirunelveli – 627012, Tamilnadu, India.

DOI:

https://doi.org/10.23755/rm.v44i0.914

Keywords:

mininorm, mininormed space, 1-norm, weight function.

Abstract

The  function on a subset  of  is the function defined by

For  , we define  .

The Hamming weight   of  is the number of non – zero coordinates of , where  From this one could see that  , where  is the 1 – norm of  given by where  . This gives a relationship between the weight function and the 1 – norm.

In this paper we establish certain properties of the weight function using the properties of norms.

References

M. MelnaFrincy and J.R.V. Edward – Extension of the – function to . Turkish Online Journal of Qualitative Inquiry . Volume 12, Issue 6, June 2021: 714-718.

Justesan and Hoholdt – A Course in Error Correcting Codes. Hindustan Bork Agency, New Delhi, 2004.

E.Kreyszig – Introductory Functional Analysis with Applications. John Wiley & Sons, New York, 1978.

B.V.Limaye – Functional Analysis, New Age International Publishers, New Delhi, 1996.

G. F. Simmons – Introduction to Topology and Modern Analysis. Mc – Graw Hill, Tokyo, 1963.

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Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

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