Abstract
© 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.
| Original language | English |
|---|---|
| Pages (from-to) | 1649-1656 |
| Journal | Discrete Mathematics |
| Volume | 340 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 1 Jul 2017 |
Keywords
- Bilinear forms graph
- Completely regular code
- Completely transitive code
- Coset graph
- Distance-regular graph
- Distance-transitive graph
- Kronecker product construction
- Lifting of a field
- Uniformly packed code
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Rifà, J., & Zinoviev, V. A. (2017). Completely regular codes with different parameters giving the same distance-regular coset graphs. Discrete Mathematics, 340(7), 1649-1656. https://doi.org/10.1016/j.disc.2017.03.001