(18, 9) Error correction code for double error correction and triple error detection

摘要

An (18, 9) error correction code that is simultaneously double error correcting and triple error detecting is disclosed. The code is defined by the following parity check matrix: ${\underset{1}{\mathrm{beta}}}^3{\underset{1}{\mathrm{beta}}}^6{\underset{1}{\mathrm{beta}}}^{12}{{\underset{1}{\mathrm{beta}}}^7}^{}{\underset{1}{\mathrm{beta}}}^{14}{\underset{1}{\mathrm{beta}}}^{11}{\underset{1}{\mathrm{beta}}}^5{\underset{1}{\mathrm{beta}}}^1{\underset{1}{\mathrm{beta}}}^2{\underset{1}{\mathrm{beta}}}^4{\underset{1}{\mathrm{beta}}}^8{\underset{1}{\mathrm{beta}}}^{16}{\underset{1}{\mathrm{beta}}}^{15}{\underset{1}{\mathrm{beta}}}^{13}{\underset{1}{\mathrm{beta}}}^9\underset{1}{0}{\underset{1}{\mathrm{beta}}}^{10}\underset{1,}{1}$ where beta is a root of the polynomial x¹⁷-1 in the finite field of 256 elements. Logic circuitry for efficiently determining the locations of single and double errors as well as for detecting the presence of uncorrectable errors is also disclosed.