Binary extremal self-dual codes of length 60 have new weight patterns
Determination of weight enumerators of binary extremal self-dual codes of length 60
Information Theory
Summary
Some special codes used in digital communications and data storage have properties that make them very reliable. These codes are called binary extremal self-dual codes, and figuring out their possible weight patterns helps understand their structure. The authors created three new codes of length 60 with weight patterns that were not known to exist before. This work fills in missing information about what weight patterns these codes can have for length 60.
What this means in practice
- •For error-correcting code designers: Identify new possible weight patterns for designing length-60 binary self-dual error-correcting codes with guaranteed extremal properties.
- •For cryptography engineers: Use the newly confirmed weight enumerators of length-60 self-dual codes to evaluate security parameters in code-based cryptographic schemes.
Authors
Masaaki Harada
Abstract
We construct three binary extremal self-dual codes of length $60$ with weight enumerators for which no binary extremal self-dual codes of length $60$ were previously known to exist. This completes the determination of the weight enumerators that occur for binary extremal self-dual codes of length $60$.