Borden Codes Research Articles

Indigenous Human Remains Database from Archaeological Sites in Québec: Preliminary Results

This paper presents the preliminary results of a project initiated by the Mohawk Council of Kahnawa:ke and the Groupe de recherche ArchéoSociale/ArchéoScience (Université de Montréal) to create a database of archaeological sites in Quebec that included Indigenous human remains. This document will be a useful tool for the repatriation/rematriation process. Using existing inventories, the database collated various data points for each site, such as the Borden code, location, date, minimal number of individuals (MNI), location of remains, reports, etc. Three site categories were identified: 1) those describing the discovery of human remains associated with Indigenous people (103 sites); 2) those with­out skeletal remains despite mentioning the presence of burial(s) (8 sites); and 3) those not reporting any information (81 sites). From these sites, information on more than 678 individuals have been collected so far. Site mapping has allowed the visualization of site distribution spatially and through time. Further research is needed to clarify the cultural affiliation and the storage location of these human remains.

Особенности обнаружения ошибок кодами Бордена

Особенности обнаружения ошибок кодами Бордена

Self-Testing Embedded Borden t-UED Code Checkers for t = 2 k q − 1 with q = 2 m − 1

Borden codes are optimal nonsystematic t-unidirectional error detecting (t-UED) codes. A possible method to design a Borden code checker is to map the Borden code words to words of an AN arithmetic code and to check the obtained words with an appropriate AN code checker. For t=q-1 with q=2m-1 we show how this method can be modified such that the Borden code checkers achieve the self-testing property under very weak conditions. It is only required that no checker input line gets a constant signal and that the Borden code words occur in a random order, making the proposed checkers very suitable for use as embedded checkers. Based on these checkers it is then possible to design embedded Borden t-UED code checkers for t=2kq-1 with q=2m-1.

Design of Embedded Self-Testing Checkers for t-UED and BUED Codes

In this article we present a new method for designing self-testing checkers for t-UED and BUED codes. The main idea of this method is to map words of the considered code to words of a code of the same type in which the value of t or the number of check bits is reduced and repeating this with the obtained words until a parity code is obtained, or to translate the code words into words of a code for which such a mapping is possible. First we consider Borden codes for t e 2k − 1, Bose, and Bose-Lin codes. The mapping operation is realized by averaging weights and check symbol values of the code words. The resulting checkers have a simple and regular structure. This structure is independent on the set of code words that is provided by the circuit under check. The checkers are very well suited for use as embedded checkers since they are self-testing with respect to single stuck-at faults under very weak assumptions. All three checker types can be tested with 2 or 3 code words. We also propose a novel approach to design checkers for Blaum codes that require much less code word tests than existing solutions.

Design of self-testing checkers for Borden codes

The optimal codes C(n,t) capable of detecting t-unidirectional errors in an n-bit vector were defined by Borden (1982). Unidirectional errors have been observed in modern digital devices such as PLAs, ROMs, and compact laser disks. In this paper, a new approach to designing self-testing checkers (STCs) for Borden codes is proposed. The new STC is built of a self-testing code-disjoint translator of the Borden code into the 1-out-of-z code (z/spl ges/2) and if z=3 or 4 an STC for the 1-out-of-n code. The translator is built of two multi-output threshold circuits with [n/2] and [n/2] inputs and a merging network. Compared to existing STCs for Borden codes the new checker generally uses significantly less hardware. It also enjoys a modular and highly regular structure which makes it attractive for VLSI implementation.

Efficient totally self-checking checkers for a class of Borden codes

In this paper a new method to design totally self-checking (TSC) checkers for a class of Borden codes is given and their applicability is discussed. The TSC checkers designed in this paper are impressively more efficient, with respect to implementation cost and speed, than the corresponding checkers hitherto proposed in the literature. >

Totally self-checking checkers for Borden codes

Abstract It is well known that a large number of errors in VLSI circuits are of the unidirectional type. Borden codes are optimal /-unidirectional error detecting (f-UED) codes. In order fully to exploit the capability of Borden codes in self-checking systems, fast and low-cost totally self-checking (TSC) checkers for such codes are necessary. However, the Borden code TSC checkers already known from the literature require excessive hardware for their implementation. In this paper we give TSC checkers for a class of Borden codes that are impressively more efficient than the corresponding TSC checkers hitherto proposed in the literature.

A totally self-checking checker for Borden's code

It is well known that a large number of errors in VLSI circuits are unidirectional in nature. J.M. Borden (Inf. Control, vol.53, p.66-73, April 1982) has studied a code for detecting only t, not all, unidirectional errors. For a code to be utilized in a self-checking system, a self-checking checker must exist for it. The totally self-checking (TSC) checker is one such checker. Many designs for TSC checkers exist for m-out-of-n codes. However, no work has been reported on the design of a TSC checker for Borden's code. The author presents such a design. They believe that this design may lead to greater applicability of Borden's code to self-checking systems. >