Self-dual Codes over the Kleinian Four Group

2000/05/26 by Höhn, Gerald · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Dual (grammatical number) #FOS: Mathematics #Finite Group Theory Research #Group (periodic table) #Group Theory (math.GR) #Kleinian group #Linguistics #Mathematics #Number Theory (math.NT) #Philosophy #Physics #Pure mathematics #Quantum Algebra (math.QA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.math/0005266

openalex publication_date 2000/05/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

Abstract

We introduce self-dual codes over the Kleinian four group K = ℤ₂ × ℤ₂ for a natural quadratic form on Kⁿ and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail.

Citations

• The Leech lattice and other lattices
• A new upper bound on the minimal distance of self-dual codes
• Orbit and coset analysis of the Golay and related codes
• Shadow bounds for self-dual codes
• Meromorphicc=24 conformal field theories

Cited by

• A Construction of Infinite Families of Self-Orthogonal Quasi-Cyclic Codes Using Constituent Codes

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