Symmetric Designs and Self‐Dual Codes | Zendy

Lander Eric S. | Zendy

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Symmetric Designs and Self‐Dual Codes

Author(s) -

Lander Eric S.

Publication year - 1981

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/s2-24.2.193

Subject(s) - divisor (algebraic geometry) , automorphism , mathematics , prime (order theory) , combinatorics , order (exchange) , multiplicative function , dual (grammatical number) , square (algebra) , discrete mathematics , geometry , mathematical analysis , art , literature , finance , economics

A construction is given for associating to any symmetric ( v, k, λ) design a self‐dual code of length v + 1 over GF ( p ), where p is any divisor of the square‐free part of k −λ. These codes are then used to obtain a substantial strengthening of a result of Hughes on automorphisms of designs. Specifically, suppose a symmetric ( v, k, λ) design possesses an automorphism σ of odd prime order q . If any prime dividing the square‐free part of k −λ has even (multiplicative) order mod q , then a must fix an odd number of points of the design.

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