# Classification of a family of completely transitive codes

@article{Gillespie2012ClassificationOA, title={Classification of a family of completely transitive codes}, author={Neil I. Gillespie and Michael Giudici and C. Praeger}, journal={ArXiv}, year={2012}, volume={abs/1208.0393} }

The completely regular codes in Hamming graphs have a high degree of combinatorial symmetry and have attracted a lot of interest since their introduction in 1973 by Delsarte. This paper studies the subfamily of completely transitive codes, those in which an automorphism group is transitive on each part of the distance partition. This family is a natural generalisation of the binary completely transitive codes introduced by Sole in 1990. We take the first step towards a classification of these… Expand

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#### References

SHOWING 1-10 OF 19 REFERENCES

Completely regular codes and completely transitive codes

- Computer Science, Mathematics
- Discret. Math.
- 1990

Neighbour transitivity on codes in Hamming graphs

- Mathematics, Computer Science
- Des. Codes Cryptogr.
- 2013

Nonexistence of completely transitive codes with error-correcting capability e>3

- Computer Science, Mathematics
- IEEE Trans. Inf. Theory
- 2001

Uniqueness of certain completely regular Hadamard codes

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2013

On q-ary linear completely regular codes with ρ=2 and antipodal dual

- Computer Science, Mathematics
- Adv. Math. Commun.
- 2010

EMBEDDING PERMUTATION GROUPS INTO WREATH PRODUCTS IN PRODUCT ACTION

- Mathematics
- Journal of the Australian Mathematical Society
- 2012

On non-antipodal binary completely regular codes

- Mathematics, Computer Science
- Discret. Math.
- 2008