環(huán)F2+uF2上線性碼及其對(duì)偶碼的二元象
The Binary Images of the Linear Codes and Their Dual Codes Over F2+uF2
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摘要: 利用環(huán)F2+uF2上線性碼C的生成矩陣給出了碼C的對(duì)偶碼C 及其Gray象(C)的生成矩陣，證明了環(huán)F2+uF2上線性碼及其對(duì)偶碼的Gray象仍是對(duì)偶碼，并由此給出了一個(gè)環(huán)F2+uF2上線性碼為自對(duì)偶碼的充要條件。
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關(guān)鍵詞:
- 線性碼; 對(duì)偶碼; 生成矩陣; Gray映射
Abstract: Based on the generator matrix of linear codes C over , F2+uF2 the generator matrixes of the dual codes C and the Gray images (C) of the linear codes C are given, and the proposition that linear codes (C) are the dual codes of (C) are showed. By using this proposition, the necessary and sufficient condition of a linear code over F2+uF2 which is self-dual is obtained. -
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