Independence of vectors in codes over rings

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• 作者：Steven T. Dougherty and Hongwei Liu
• 关键词：Frobenius rings ; Principal ideal rings ; Codes over rings ; Chinese Remainder Theorem
• 刊名：Designs, Codes and Cryptography
• 出版年：2009
• 出版时间：April, 2009
• 年：2009
• 卷：51
• 期：1
• 页码：55-68
• 全文大小：188.9 KB

文摘

We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to the product of local Frobenius rings and use this decomposition to describe an analog of linear independence. Special attention is given to codes over principal ideal rings and a basis for codes over principal ideal rings is defined. We prove that a basis exists for any code over a principal ideal ring and that any two basis have the same number of vectors.