中文摘要：

设Fq是q元有限域,q是素数的幂。令信源集S为Fq上所有的n×n矩阵的等价标准型,编码规则集ET和解码规则集ER为Fq上所有的n×n非奇异矩阵对,信息集为Fq上所有的n×n非零的奇异矩阵,构造映射f：S×ET→M g：M×ER→S∪{欺诈}（Sr,（P,Q））｜→PSrQ,（A,（X,Y））｜→Sr,如果XKAKY=Sr,秩A=r欺诈,其他其中K=In-100 0。证明了该六元组（S,ET,ER,M;f,g）是一个带仲裁的Cartesian认证码,并计算了该认证码的参数。进而,当收方与发方的编码规则按照等概率均匀分布选取时,计算出该码的概率PI,PS,PT,PR0,PR1。

英文摘要：

Let Fq be the finite field with q elements,where q is a power of a prime.Suppose the set of source states S is formed by all equivalent normal forms of n×n matrices over Fq,the set of encoding rules ET and decoding rules ER are formed by all pairs of the n×n nonsingular matrix over Fq,and the set of messages M is formed by all n×n both nonzero and singular matrices over Fq.Construct the mapsf：S×ET→Mg：M×ER→S∪{reject}（Sr,（P,Q））｜→PSrQ,（A,（X,Y））｜→Sr,if XKAKY=Sr,rank（A）=r,reject,otherwise,where K=In-1000.The six tuple（S,ET,ER,M;f,g）,which is a Cartesian authentication code with arbitration,is constructed,and the associated parameters are calculated.Moreover,the encoding rules obey a uniform probability distribution,and PI,PS,PT,PR0 and PR1 are computed.