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

1 Scopus citations

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

Access to Document

10.1007/BF01389355

Cite this

@article{a3bcedc3307541a9931dc50b6c1b523b,

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.",

author = "Skinner, \{Chris M.\}",

year = "1993",

month = mar,

doi = "10.1007/BF01389355",

language = "English (US)",

volume = "3",

pages = "63--68",

journal = "Designs, Codes and Cryptography",

issn = "0925-1022",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Non-symmetric 2-designs modulo 2

AU - Skinner, Chris M.

PY - 1993/3

Y1 - 1993/3

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.

UR - https://www.scopus.com/pages/publications/34250075459

UR - https://www.scopus.com/inward/citedby.url?scp=34250075459&partnerID=8YFLogxK

U2 - 10.1007/BF01389355

DO - 10.1007/BF01389355

M3 - Article

AN - SCOPUS:34250075459

SN - 0925-1022

VL - 3

SP - 63

EP - 68

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

IS - 1

ER -

Non-symmetric 2-designs modulo 2

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this