In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Hadamard matrix over the kth
roots of unity, we can construct a larger Butson matrix over the ℓth
roots of unity for any ℓ
dividing k, provided that any prime p dividing k also divides ℓ
. We prove that a Zps
-additive code with p a prime number is isomorphic as a group to a BH-code over Zps
and the image of this BH-code under the Gray map is a BH-code over Zp
(binary Hadamard code for p=2
). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided.
Open Access funding provided by CRUE-CSIC agreement with Springer Nature., Project FQM-016 funded by JJAA (Spain)., Spanish grant PID2019-104664GB-I00 (AEI/FEDER, UE)., Irish Research Council (Government of Ireland Postdoctoral Fellowship, GOIPD/2018/304)
ID Code:
28744
Deposited On:
19 Jul 2023 14:07 by
Vidatum Academic
. Last Modified 19 Jul 2023 14:07