Non-symmetric 2-designs modulo 2

Chris M. Skinner

doi:10.1007/BF01389355

Non-symmetric 2-designs modulo 2

Chris M. Skinner

Research output: Contribution to journal › Article › peer-review

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Abstract

Necessary conditions are obtained for the existence of a 2 - (v, k, λ) design, for which the block intersection sizes s₁, s₂, ..., s_n satisfy s₁ ≡s₂ ≡ ... ≡s_n ≡s (mod 2^e), where e is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.

Original language	English (US)
Pages (from-to)	63-68
Number of pages	6
Journal	Designs, Codes and Cryptography
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/BF01389355
State	Published - Mar 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computer Science Applications
Applied Mathematics

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10.1007/BF01389355

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title = "Non-symmetric 2-designs modulo 2",

abstract = "Necessary conditions are obtained for the existence of a 2 - (v, k, λ) design, for which the block intersection sizes s1, s2, ..., sn satisfy s1 ≡s2 ≡ ... ≡sn ≡s (mod 2e), where e is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.",

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N2 - Necessary conditions are obtained for the existence of a 2 - (v, k, λ) design, for which the block intersection sizes s1, s2, ..., sn satisfy s1 ≡s2 ≡ ... ≡sn ≡s (mod 2e), where e is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.

AB - Necessary conditions are obtained for the existence of a 2 - (v, k, λ) design, for which the block intersection sizes s1, s2, ..., sn satisfy s1 ≡s2 ≡ ... ≡sn ≡s (mod 2e), where e is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.

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Non-symmetric 2-designs modulo 2

Abstract

All Science Journal Classification (ASJC) codes

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