在信息理论中，最优线性码具有很强的纠错能力、低相关性线性序列在密码系统和CDMA通信系统中得到了广泛应用。因此构造最优线性码和构造低相关性线性序列具有重要的研究价值。记 R＝ Fp＋ uFp ，这里的 p为奇素数。本文首先通过迹映射构造出环 R上的一类新的线性码，然后将这类新的线性码的删余码通过Gray映射得到了域 Fp上一类最优码。同时，通过迹映射构造出环 R上的一类线性循环码，将这类线性循环码视为线性周期序列并通过广义Nechaev-Gray映射得到了域 Fp上一类低相关线性周期序列。%In information theory ,optimal linear codes have good capability in error-correcting in coding theory and linear se-quences with low correlation have been widely used in cryptography and CDMA systems .Therefore ,it has great value to study the construction of optimal linear codes and low correlation linear sequences .Let R= Fp+ uFp ,where p is an odd prime .A class of new linear codes over R is constructed by means of the trace map .Then a kind of optimal codes over Fp is obtained via the Gray map from the punctured new linear codes .Furthermore ,a class of new linear cyclic codes over R is also constructed by means of the trace map .A kind of low correlation linear sequences over Fp is observed via the generalized Nechaev-Gray map from the class of new linear cyclic codes ,which are regarded as a class of linear periodic sequences .
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