Generalized Bose–Lin Codes, a Class of Codes Detecting Asymmetric Errors

Bose and Lin introduced a class of systematic codes for detection of binary asymmetric errors. In this note, we describe a generalization to q-ary asymmetric error detecting codes. For these codes, the possible undetectable errors are characterized and the undetectable errors of minimum weight are determined     

Sensitivity analysis in bayesian classification models: multiplicative deviations

The sensitivity of Bayesian pattern recognition models to multiplicative deviations in the prior and conditional probabilities is investigated for the two-class case. Explicit formulas are obtained for the factor K by which the computed posterior probabilities should be divided in order to eliminate the deviation effect. Numerical results for the case of binary features indicate that the Bayesian model tolerates large deviations in the prior and conditional probabilities. In fact, the a priori ratio and the likelihood ratio may deviate within a range of 65-135 percent and still produce posterior probabilities in accurate proximity of at most ±0.10. The main implication is that Bayesian systems which are based on limited data or subjective probabilities are expected to have a high percentage of correct classification despite the fact that the prior and conditional probabilities they use may deviate rather significantly from the true values.     

A Generic Construction of Cartesian Authentication Codes

In this paper, a coding-theory construction of Cartesian authentication codes is presented. The construction is a generalization of some known constructions. Within the framework of this generic construction, several classes of authentication codes using certain classes of error-correcting codes are described. The authentication codes presented in this paper are better than known ones with comparable parameters. It is demonstrated that the construction is related to certain combinatorial designs, such as difference matrices and generalized Hadamard matrices     

Bounds on the worst case probability of undetected error

Upper and lower bounds on the average worst-case probability of undetected error for linear [n,k,q] codes are given     

The worst case probability of undetected error for linear codes onthe local binomial channel

The worst case probability of undetected error for a linear [n,k:q] code used on a local binomial channel is studied. For the two most important cases it is determined in terms of the weight hierarchy of the code. The worst case probability of undetected error is determined explicitly for some classes of codes     

On the second greedy weight for linear codes of dimension at least 4

The maximum of g/sub 2/ - d/sub 2/ for linear [n,k,d;q] codes C is studied. Here d/sub 2/ is the smallest size of the support of a two-dimensional subcode of C and g/sub 2/ is the smallest size of the support of a two-dimensional subcode of C which contains a codeword of weight d. For codes of dimension 4 or more, upper and lower bounds on the maximum of g/sub 2/-d/sub 2/ are given.     

Constructing Proper Codes for Error Detection

It is shown that for any alphabet size q and any code size M, there exist proper codes for error detection on a q-ary symmetric channel for all sufficiently large lengths. The stronger condition zero-strong proper code is defined. It is shown that such codes can only exist for q dividing M, and if this is the case they are shown to exist for sufficiently large lengths. The existence proofs are constructive.     

Weight hierarchies of extremal non-chain binary codes of dimension4

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d₁,d₂,···,d_k ) where d_r is the smallest support of an r-dimensional subcode of C. An [n,k;q] code is extremal nonchain if, for any r and s, where 1⩽rS(D)=d_r, and w_S (E)=d_s. The possible weight hierarchies of such binary codes of dimension 4 are determined     

Three-dimensional optical tomographic imaging of breast in a humansubject

We present for the first time a full three-dimensional (3-D) reconstruction of absorption images of breast from continuous-wave (cw) measurements performed on a premenopausal woman. Our 3-D optical images clearly reveal a large primary tumor as well as a small secondary tumor in a separate location of the breast. The multiple tumors identified by our 3-D optical imaging have been confirmed by the subsequent biopsy examination of the breast. Quantitative information of the optical images obtained is provided in terms of the location, size, and absorption coefficient of the tumors.     

The simplex codes and other even-weight binary linear codes for error correction

The probability of correct decoding on the binary-symmetric channel is studied. In particular, a class of codes with the same lengths and dimensions as the linear simplex codes, but with larger probability of correct decoding for all parameters p, 0 < p < 1/2, is given.