Algebraic Coding Theory Over Finite Commutative Rings by Steven T. Dougherty

Author:Steven T. Dougherty
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.16)

Then extend the map coordinatewise to .

We shall define another Gray map also defined for X-rings. This map will turn out to be conjugate to the previously defined Gray map. We keep two maps because often it is much easier to find results using one of the maps as opposed to the other.

Let R be an X-ring with . We define the map . View R as a vector space over with basis where . Define where

Extend linearly to be defined over the entire ring R. Specifically,

(4.17)

As an example, if the subsets are ordered as

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