Коды, исправляющие ошибки. Простейшие границы. Коды Варшамова—Тененгольца

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. . . . . , . , . , : , .

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<ul><li> 1. , 2013 www.dainiak.com </li></ul> <p> 2. , : ( ) ( ) (, ) ( ); 3. : : ? : : 4. , : ( ) ( ) : 0,1 5. , = . - ( ) ( ) , .. = 2 = 0,1 . , .. # 0 6. / . , , . , ( ). , , &gt; . 7. / , ( , ). : , , : , , 8. , : , , = , , &gt; 0 , = 0 , , , , + , . , , , , , . 9. , (), , = , , , # , , 10. /, : , min # , : , = 1 , = 3 11. , . min , , : &gt; &gt; 2 12. , , . , . .., : 13. . .., , : 14. , : , , , . , : ( ) 15. , : , , , . , , , . 16. , / 17. : 1 2 =1 0 mod + 1 ( ) = 1 2 +1 | +1 2 +1 , / . 18. : .. , . = 1 , 1 1 = 1 1 +1 ( ). : . 19. : , , . , = 1001, = 10001, , . 0 # &gt; = 0 1 # &gt; = 1 , = 0, , 1. , = 1, , 0. 20. : =1 =1 1 , = =1 =1 1 + = 1 +1 = = =+1 1 = + =+1 21. : = + =+1 = 1 0 mod + 1 , 1 mod + 1 = 0, 1. = 1, 1 + = 0 + = 0 22. : , = 0, mod + 1 = 1, = 1, mod + 1 = 0. , . , 1, 1 0 1 &lt; 0. , mod + 1 , 1, 0. 23. : : =1 1 mod + 1 , - 0. &gt; , - 1. 24. : , : = +1 ( = 0, = ; = , = ) = + + 1 + &gt; , + 1 + &gt; = + 1 + 1 mod + 1 . 25. : = +1 + 1 + 1 mod + 1 . , = 0: + 1 + 1 = 0. = 0 +1 = = = 0. + 1 + 1 = + 1. = 1 +1 = = = 1. . 26. : = +1 + 1 + 1 , = &gt; 0. : 1 = = = = 0 1 = = = = 1 , = , . 27. : = +1 + 1 + 1 0 &lt; . = 0, = 1 &lt; . = 1, = + 1 + 1 &gt; . , = + 1 + 0 = + 1 0. . 28. ..: &gt; : 1 2 =1 0 mod , : 1 2 =1 =1 2 0 mod 29. . , 0 1 1 0. . () . 1 2, 2 1. , , . 30. : - 0 1, mod + 1 - 1 0, mod + 1 ( .) 31. , , , . - , , : , , - , . 32. . ( (R.W. Hamming), ) , , - 1 2 2 =0 1 2 , , . 33. : = 1, 2, , , , -. = , 1 2 : 1 2 =1 1 2 = 1 2 34. - . ( , ) , , , , . , , -. 35. - : = 1, , . ( , ). =1 , . 1 2 3 36. . (R.C. Singleton) , , - +1 , , MDS- (maximum distance separable codes). 37. : = 1, , , , -. =1 , 1 . , , , . - + 1 . +1. 38. : , </p>