© 2016, Springer Science+Business Media New York. Let C be a Z2Z4-additive code of length n> 3. We prove that if the binary Gray image of C is a 1-perfect nonlinear code, then C cannot be a Z2Z4-cyclic code except for one case of length n= 15. Moreover, we give a parity check matrix for this cyclic code. Adding an even parity check coordinate to a Z2Z4-additive 1-perfect code gives a Z2Z4-additive extended 1-perfect code. We also prove that such a code cannot be Z2Z4-cyclic.
- Perfect codes
- Simplex codes
- Z Z -additive cyclic codes 2 4