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01.09.2015 | Ausgabe 3/2015

# Completely reducible super-simple designs with block size five and index two

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 3/2015
Autoren:
Hengjia Wei, Hui Zhang, Gennian Ge
Wichtige Hinweise
Communicated by L. Teirlinck.

## Abstract

Complete reducible super-simple (CRSS) designs are closely related to $$q$$-ary constant weight codes. A $$(v,k,\lambda )$$-CRSS design is just an optimal $$(v,2(k-1),k)_{\lambda +1}$$ code. In this paper, we mainly investigate the existence of a $$(v,5,2)$$-CRSS design and show that such a design exists if and only if $$v\equiv 1,5\pmod {20}$$ and $$v\ge 21$$, except possibly when $$v = 25$$. Using this result, we determine the maximum size of an $$(n,8,5)_3$$ code for all $$n\equiv 0,1,4,5 \pmod {20}$$ with the only length $$n=25$$ unsettled. In addition, we also construct super-simple $$(v,5,3)$$-BIBDs for $$v=45,65$$.

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