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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
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Optimal Quaternary Hermitian LCD Codes.

Liangdong Lu1, Ruihu Li1, Yuezhen Ren1

  • 1Fundamentals Department, Air Force Engineering University, Xi'an 710051, China.

Entropy (Basel, Switzerland)
|May 24, 2024
PubMed
Summary

This study presents new tables of quaternary Hermitian linear complementary dual (LCD) codes. These codes are valuable for enhancing security in cryptosystems against side-channel attacks.

Keywords:
Hermitianlinear codelinear complementary dualoptimalquaternary code

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Area of Science:

  • Coding Theory
  • Cryptography
  • Information Security

Background:

  • Linear complementary dual (LCD) codes are a class of linear codes.
  • LCD codes are increasingly recognized for their role in countering side-channel attacks on embedded cryptosystems.

Purpose of the Study:

  • To present tables of good quaternary Hermitian LCD codes.
  • To utilize these codes in constructing new types of codes (puncturing, shortening, combination).
  • To identify optimal and near-optimal codes within a specific range.

Main Methods:

  • Systematic generation and tabulation of quaternary Hermitian LCD codes.
  • Analysis of code properties including optimality and bounds adherence.
  • Application of code construction techniques.

Main Results:

  • Three tables of the best-known quaternary Hermitian LCD codes for lengths n≤25 are provided.
  • Many presented codes are optimal or near-optimal, meeting or approaching theoretical bounds.
  • Demonstrated utility in constructing advanced code types.

Conclusions:

  • The presented codes offer significant advancements in the field of LCD codes.
  • These findings contribute to the development of more secure cryptographic systems.
  • The tables serve as a valuable resource for researchers and practitioners.