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Linear Codes from Two Weakly Regular Plateaued Balanced Functions.

Shudi Yang1, Tonghui Zhang1, Ping Li2

  • 1School of Mathematical Sciences, Qufu Normal University, Jining 273165, China.

Entropy (Basel, Switzerland)
|February 25, 2023
PubMed
Summary
This summary is machine-generated.

This study constructs linear codes with few weights using weakly regular plateaued balanced functions. These new codes are minimal and beneficial for secret sharing schemes.

Keywords:
Walsh transformlinear codeplateaued balanced functionweight distribution

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Area of Science:

  • Coding Theory
  • Cryptography
  • Discrete Mathematics

Background:

  • Linear codes with few weights are crucial in cryptography and secret sharing.
  • Existing constructions often lack specific properties or are complex.

Purpose of the Study:

  • To construct a novel family of linear codes with a limited number of nonzero weights.
  • To analyze the properties, specifically minimality, of the newly constructed codes.
  • To evaluate their applicability in secret sharing schemes.

Main Methods:

  • Utilizing defining sets derived from two distinct weakly regular plateaued balanced functions.
  • Applying a generic construction method for linear codes.
  • Investigating the minimality of the resulting codes.

Main Results:

  • A family of linear codes with at most five nonzero weights was successfully constructed.
  • The minimality of these codes was rigorously examined.
  • The constructed codes demonstrate potential utility in secret sharing applications.

Conclusions:

  • The proposed method provides a valuable approach to generating linear codes with few weights.
  • The constructed codes offer improved properties for cryptographic applications, particularly secret sharing.