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On the largest minimum distances of [n,6] LCD codes.
1Air Defense and Antimissile School, Air Force Engineering University, Xi'an, Shaanxi 710051, China.
Linear complementary dual (LCD) codes offer security against side-channel attacks. This study determines the minimum weights for binary LCD codes of dimension 6, providing crucial parameters for secure coding applications.
Area of Science:
- Coding Theory
- Cryptography
- Information Security
Background:
- Linear complementary dual (LCD) codes are essential for constructing codes resistant to side-channel and fault injection attacks.
- Optimal linear codes and LCD codes are fundamental in error correction and secure communication systems.
Purpose of the Study:
- To determine the exact minimum weights () for binary LCD codes of length and dimension 6.
- To investigate the nonexistence and construction of LCD codes with specific parameters.
Main Methods:
- Utilizing theories of defining vectors, generalized anti-codes, reduced codes, and nested codes.
- Analyzing the properties of binary linear and LCD codes.
Main Results:
- The exact value of is determined for .
- Inequalities for are established for and .
Conclusions:
- The research provides precise minimum weight values for specific LCD codes, crucial for cryptographic applications.
- The findings contribute to the understanding and construction of secure coding schemes.
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