ℤ4-codes and their Gray map images as orthogonal arrays
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A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter.Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over ℤ4 and their (usually non-linear) binary Gray map images.We show that Delsarte's observation extends to codes over arbitrary finite commutative rings with identity. Also, we show that the strength of the Gray map image of a ℤ4 code is one less than the minimum Lee weight of its Gray map image.
Cameron , P J , Kusuma , J & Solé , P 2017 , ' ℤ 4 -codes and their Gray map images as orthogonal arrays ' , Designs, Codes and Cryptography , vol. 84 , no. 1-2 , pp. 109-114 . https://doi.org/10.1007/s10623-016-0225-4
Designs, Codes and Cryptography
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