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Acta Mathematicae Applicatae Sinica English Series

Error detection capability of shortened hamming codes and their dual codes

Xia Shutao, Fu Fangwei

Published Jul 1, 2000• 4 citations
Publisher
DOI
10.1007/bf02679894

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東京工芸大学工学部紀要•Jan 1, 2008•1 citation
The monotonic property of the probability of undetected error is considered when a shortened code of a linear code over GF(q) is used for error detection on a q-ary symmetric channel. Some conditions are presented under which the probability of undetected error is (or is not) monotonic with respect to the code length or the symbol error probability. It is shown that the probability of undetected error for a maximum distance separable code is monotonic with respect to the codelength. It is also shown that the probability of undetected error of a shortened code of any binary cyclic Hamming code generated by a trinomial is not monotonic with respect to the bit-error rate if the code length is short.>
All Error Detecting Modified Hamming Codes for Ideal Optical Channel and Application to Practical SystemChugo Fujihashi *1 Modified Hamming Codes designed to have the capability of all error detecting and one error correcting on an ideal optical channel are presented.The codes are applicable to an optical channel with only quantum noise, and are able to achieve all error excluding transmission on the optical channel in a future advanced communication system.The codes are obtained from the Modified of ordinary (7, 4) Hamming codes by adding an extra one-bit symbol to make all errors detectable.It is shown that the codes are also useful on a practical level to completely exclude almost all errors on a channel affected by not only quantum noise but also external noise.
Modified Hamming Codes designed to have the capability of all error detecting and one error correcting on an ideal optical channel are presented. The codes are applicable to an optical channel with only quantum noise, and are able to achieve all error excluding transmission on the optical channel in a future advanced communication system. The codes are obtained from the Modified of ordinary (7, 4) Hamming codes by adding an extra one-bit symbol to make all errors detectable. It is shown that the codes are also useful on a practical level to completely exclude almost all errors on a channel affected by not only quantum noise but also external noise.