The focus of this bachelor thesis are maximum distance separable codes. A code is used to communicate over noise channel so any interferences that may occur can be detected and corrected. Maximum distance separable codes have a capacity to correct many errors. Maximum distances separable codes are usually constructed as linear codes over fields but in this text we will also consider them over certain commutative rings. Recently it has been proven that all linear maximum distance separable codes over prime fields are short and we will prove that this carries over to certain linear maximum distance separable codes over p-adic rings.
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