On the integral ring spanned by genus two weight enumerators

It is known that the weight enumerator of a self-dual doubly even code in genus g=1 can be uniquely written as an isobaric polynomial in certain homogeneous polynomials with integral coefficients. We settle the case where g=2 and prove the non-existence of such polynomials under some conditions.     

GOB designs for authentication codes with arbitration

Combinatorial characterization of optimal authentication codes with arbitration was previously given by several groups of researchers in terms of affine α-resolvable + BIBDs and α-resolvable designs with some special properties, respectively. In this paper, we revisit this known characterization and restate it using a new idea of GOB designs. This newly introduced combinatorial structure simplifies the characterization, and enables us to extend Johansson’s well-known family of optimal authentication codes with arbitration to any finite projective spaces with dimension greater than or equal to 3.     

Group Codes Defined on Totally Ordered Sets

ＧｒｏｕｐＣｏｄｅｓＤｅｆｉｎｅｄｏｎＴｏｔａｌｌｙＯｒｄｅｒｅｄＳｅｔｓＷａｎＺｈｅｘｉａｎ（万哲先）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ，１０００８０ａｎｄＤｅｐａｒｔｍｅｎｔｏｆＩｎ...     

环Z/p\+kZ上m阶交错矩阵的计数定理及其应用

设W\-m(R)是有限局部环R=Z/p\+kZ上所有m阶交错矩阵所构成的集合（p是素数,k>1）. 该文通过确定R上任意m阶交错矩阵的标准形,计算出W\-m(R)在线性群GL\-m(R)作用下的轨道数及n(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)]),其中W（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])(∑[DD(]l[]i=1[DD)]s\-i=t)表示不变因子为（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])的所有m阶交错矩阵构成的集合,n(2r,2t,（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])表示其中的元素个数. 最后,作者利用有限局部环R上交错矩阵的标准形构作了一个Cartesian认证码,并计算出其全部参数.     

Weight enumerators,intersection enumerators,and Jacobi polynomials

The intersection enumerator and the Jacobi polynomial in an arbitrary genus for a binary code are introduced. Adding the weight enumerator into our discussion, we give the explicit relations among them and give some of their basic properties.     

Use of Chemometrics: Principal Component Analysis (PCA) and Principal Component Regression (PCR) for the Authentication of Orange Juice

ABSTRACT

Principal Component Analysis (PCA) was applied to a set of physico-chemical variables obtained from 41 samples of summer orange juice, in order to reduce the number of variables. Working with the covariance matrix, three components (which explained 98.27% of the variance) were taken. With the correlation matrix, four components which explained: 85.65% of the variance were taken. With the scores corresponding to both matrixes a principal component regression (PCR) was carried out against the dependent variable of Brix grades, so as to obtain two statistical models that would allow the detection of adulterations in pure orange juice, based on dilution and later masking by the addition of sugar. The models were tested with simulated dilutions of 41 samples of juice, to assess the effectiveness of each for the detection of adulterations. Both models turned out to be equally effective, detecting adulterations starting from about 15 % of dilution.