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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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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (p - 1)/2.

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This summary is machine-generated.

Researchers constructed a new infinite family of linear codes with few weights using specific plateaued functions. These codes are valuable for cryptography and coding theory applications, offering minimal properties.

Keywords:
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Area of Science:

  • Coding Theory
  • Cryptography
  • Number Theory

Background:

  • Linear codes are fundamental in cryptography and coding theory.
  • Codes with few weights have diverse applications, including authentication and secret sharing.
  • Plateaued functions are crucial in constructing cryptographic primitives.

Purpose of the Study:

  • To construct an infinite family of linear codes with few weights.
  • To analyze the properties of these codes, specifically their weight distributions.
  • To explore the applicability of these codes in cryptographic and theoretical contexts.

Main Methods:

  • Construction of linear codes using two distinct weakly regular unbalanced (and balanced) plateaued functions.
  • Setting the parameter p such that p ≡ 1 (mod 4).
  • Utilizing exponential sums and Walsh transform for analysis.

Main Results:

  • An infinite family of linear codes was successfully constructed.
  • The weight distributions of the constructed codes were completely determined.
  • Most of the codes exhibit few nonzero weights and are minimal.

Conclusions:

  • The study presents a novel construction for linear codes with desirable properties.
  • The findings contribute to the understanding of code properties and their applications.
  • The constructed codes offer potential for advancements in cryptography and coding theory.