Existence of directed BIBDs with block size 7 and related perfect 5-deletion-correcting codes of length 7

Authors:
R. J. Abel;F. E. Bennett
Affiliations:
School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052;Department of Mathematics, Mount Saint Vincent University, Halifax, Canada B3M 2J6
Venue:
Designs, Codes and Cryptography
Year:
2010

Citing 5
Cited 0

All directed GDDs with block size three, λ1=0,exist

Utilitas Mathematica
On the construction of perfect deletion-correcting codes using design theory

Designs, Codes and Cryptography
Balanced Incomplete Block Designs with Block Size 7

Designs, Codes and Cryptography
Combinatorial and algorithmic aspects of directed designs

Combinatorial and algorithmic aspects of directed designs
Constructions for Perfect 5-Deletion-Correcting Codes of Length

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Wang and Yin have established the existence of a directed BIBD with block size 7 and index 1 (a DBIBD(v, 7, 1)) for all v 驴 1, 7 (mod 21) except for v = 22 and possibly for 68 other cases. In this paper, we reduce the number of possible exceptions to 4, namely v = 274, 358, 400, 526. Correspondingly, for all such v, our results establish the existence of a T(2, 7, v)-code or equivalently a perfect 5-deletion-correcting code with words of length 7 over an alphabet of size v, where all the coordinates must be different. In the process, we also reduce the possible exceptions for (v, 7, 2)-BIBDs to 2 cases, v = 274 and 358 (in addition to the non-existent (22, 7, 2)-BIBD).