✦ LIBER ✦

Binary codes and caps

✍ Scribed by Aiden A. Bruen; Lucien Haddad; David L. Wehlau

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 177 KB
Volume: 6
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1998)6:4<275::aid-jcd5>3.0.co;2-c

No coin nor oath required. For personal study only.

✦ Synopsis

The connection between maximal caps (sometimes called complete caps) and certain binary codes called quasi-perfect codes is described. We provide a geometric approach to the foundational work of Davydov and Tombak who have obtained the exact possible sizes of large maximal caps. A new self-contained proof of the existence and the structure of the largest maximal nonaffine cap in PG(n, 2) is given. Combinatorial and geometric consequences are briefly sketched. Some of these, such as the connection with families of symmetric-difference free subsets of a finite set will be developed elsewhere.

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