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Linear Codes over the Finite Ring <i>Z</i><sub>15</sub>
Langfang Normal University, Langfang, China
Langfang Normal University, Langfang, China
Langfang Normal University, Langfang, China
Langfang Normal University, Langfang, China
Langfang Normal University, Langfang, China
- 1 Langfang Normal University, Langfang, China
- 2 Langfang Normal University, Langfang, China
- 3 Langfang Normal University, Langfang, China
- 4 Langfang Normal University, Langfang, China
- 5 Langfang Normal University, Langfang, China
Advances in Linear Algebra & Matrix Theory·Volume 10 (2020)·Pages 1–5·Published 8 April 2020·DOI10.4236/alamt.2020.101001
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Abstract
In this paper, the structure of the non-chain ring Z 15 is studied. The ideals of the ring Z 15 are obtained through its non-units and the Lee weights of elements in Z 15 are presented. On this basis, by the Chinese Remainder Theorem, we construct a unique expression of an element in Z 15 . Further, the Gray mapping from Z n 15 to Z 2n 15 is defined and it’s shown to be distance preserved. The relationship between the minimum Lee weight and the minimum Hamming weight of the linear code over the ring Z 15 is also obtained and we prove that the Gray map of the linear code over the ring Z 15 is also linear.
KeywordsLee WeightHamming WeightGray MapDual Code
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