Linearly representable codes over chain rings

In this paper, we consider linear codes over finite chain rings. We present a general mapping which produces codes over smaller alphabets. Under special conditions, these codes are linear over a finite field. We introduce the notion of a linearly representable code and prove that certain MacDonald codes are linearly representable. Finally, we give examples for good linear codes over finite fields obtained from special multisets in projective Hjelmslev planes.

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