On Symmetric Error Correcting and All Unidirectional Error Detecting Codes

AbstmctThis paper considers the design of binary Mock codes that are capaMe of correcting UP to t symmetric errors and detecting all unidirectional errors. A class of systematic t symmetric-error-correctingM1-unidirectional-error-detecting (tS~ECIAUED) codes are proposed. When = o the proposed codes become Berger codes. For t = 1, the proposed codes are puts. t-symmetric-errorcorrecting/all-unidirectional-errordetecting (t-SyECIAUED) codes were proposed for applications in digital systems [31-[51, [71-[1~1, [141-[16] with the objective that if there are fewer than or equal to t errors, all of them could be corrected and if there are more than t errors shown to be of “asymptotically optimal order.” Methods to construct nonsystematic t-SyECIAUED codes for t = 2 and 3 are also presented in this paper.