Information Theory
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Equivalence and Generalization of Self-Dual Code Constructions via Isotropic Lines and Lean Formalization
This paper establishes the equivalence between Kim's building-up construction and Chinburg-Zhang's Hilbert symbol construction for binary self-dual codes. It then introduces a q-ary generalization of the Chinburg-Zhang construction, enabling efficient construction of q-ary self-dual codes over split…
Concatenated Ternary Codes Yield Superior Nonlinear and Linear Constructions for Asymmetric Channels
New generalized concatenation methods construct nonlinear single-error-correcting codes for binary asymmetric channels using ternary outer codes, outperforming some Varshamov-Tenengol'ts-Constantin-Rao codes in many cases. For nonbinary asymmetric channels, the approach yields linear codes superior …