Construction and analysis of check matrices correcting single and double adjacent errors codes

Annotation: One of the consequences of the impact of space radiation on the on-board system equipment of spacecraft is a memory faults. Due to the decrease in the design standards of digital electronic component base, the number of multiple memory faults, in par-ticular double ones, is increasing. To protect against double memory faults, the codes that correct single and double adjacent errors are used. The paper presents the mathematical basis for the use of codes of this type. A statement about the structure of the check matrix necessary to correct single and double adjacent errors is proposed and proven. A general algorithm for finding and correcting single and double adjacent errors in a memory code word is formulated. The statement about the minimum number of check bits for an information word of any length is proven. A general assessment of the complexity of coding op-erations and error correction in a code word has been carried out depending on the number of check bits and the structures of check matrices. The results of the work can be used to design the devices detecting and correcting errors in the on-board memory of spacecraft.

Keywords: single and double adjacent errors correction codes, error-control codes, multiple faults, space electronics