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An Algebraic Method for Constructing Latin Squares and LDPC Codes | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 تیر 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.31310.1822 | ||
| نویسنده | ||
| A Talebi* | ||
| تاریخ دریافت: 27 بهمن 1404، تاریخ بازنگری: 09 تیر 1405، تاریخ پذیرش: 16 تیر 1405 | ||
| چکیده | ||
| In this paper, first, an algebraic method for constructing Latin squares is presented. Using this method, a large family of Latin squares with distinctive properties is obtained. These Latin squares are constructed using a base matrix derived from dihedral groups. using the cyclic subgroups of D2n, new Latin squares with special properties can be constructed. Then, based on these squares, quasi-cyclic LDPC codes with girth 6 are constructed. These codes perform well with iterative decoding algorithms. This construction method is suitable for building high-rate codes whose parity-check matrices have low column weight. Finally, an algorithm for generating generator matrices using Python is introduced. | ||
| کلیدواژهها | ||
| LDPC codes؛ generator matrix؛ parity-check matrix؛ Latin square | ||
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آمار تعداد مشاهده مقاله: 6 |
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