特征为3的有限域上最优LRC码

Optimal LRC Codes over Finite Fields with Characteristic 3

局部恢复(LRC)码是一类线性码,当码字中某个分量的值丢失时,可通过访问该码字中其他少数(至多r个)分量来恢复。首先在有限域F_(27)上分别运用加法子群和乘法子群作陪集的方法构造LRC码,并且得出这些LRC码是最优的;进一步推广到特征为3的一般有限域F_(3l)上来构造一簇最优LRC码。最后,将构造的这些码与同类最新成果的LRC码的局部恢复性进行比较,结果表明,构造的LRC码具有更好的局部恢复性。

Local recovery codes(LRC)are a class of linear codes.When the value of a component in the codeword is lost,it can be recovered by accessing a few(at most r)other components in the codeword.In this paper,we first construct LRC codes by using additive subgroups and multiplication subgroups as cosets on finite field F_(27),and obtain that these LRC codes are optimal;Furthermore,we generalize to construct a cluster of optimal LRC codes for a general finite field F_(3l) with characteristic 3.Finally,the local resilience of these codes is compared with the latest LRC codes of the same kind.The results show that the constructed LRC codes have better local resilience.