MinT - Information on Result #1200293

Information on Result #1200293

Linear OOA(49³⁵, 8388602, F₄₉, 9, 6) (dual of [(8388602, 9), 75497383, 7]-NRT-code), using OOA stacking with additional row based on linear OOA(49³⁵, large, F₄₉, 3, 6), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(49⁰, s, F₄₉, 3, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
3. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
4. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
5. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
6. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
7. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
8. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
9. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
10. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
11. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
12. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
13. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
14. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
15. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
16. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
17. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
18. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
19. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
20. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
21. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
22. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
23. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
24. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
25. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
26. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
27. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
28. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
29. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
30. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
31. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
32. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
33. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
34. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
35. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
36. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
37. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
38. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
39. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
40. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
41. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
42. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
43. linear OOA(49⁰, 120100, F₄₉, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
44. linear OOA(49¹, 120100, F₄₉, 3, 1) (dual of [(120100, 3), 360299, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(49¹, s, F₄₉, 3, 1) for arbitrarily large s, using
    - appending 2 arbitrary columns [i] based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
45. linear OOA(49¹, 120100, F₄₉, 3, 1) (dual of [(120100, 3), 360299, 2]-NRT-code) (see above)
46. linear OOA(49¹, 120100, F₄₉, 3, 1) (dual of [(120100, 3), 360299, 2]-NRT-code) (see above)
47. linear OOA(49⁴, 120100, F₄₉, 3, 2) (dual of [(120100, 3), 360296, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(49⁴, 120100, F₄₉, 2, 2) (dual of [(120100, 2), 240196, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(49⁴, 120100, F₄₉, 2) (dual of [120100, 120096, 3]-code), using
      - Hamming code H(4,49) [i]
48. linear OOA(49⁷, 1921601, F₄₉, 3, 3) (dual of [(1921601, 3), 5764796, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(49⁷, 5769602, F₄₉, 3, 3) (dual of [(5769602, 3), 17308799, 4]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OA(49⁷, 5769603, F₄₉, 3) (dual of [5769603, 5769596, 4]-code or 5769603-cap in PG(6,49)), using
      - product of two caps with tangent hyperplane [i]
49. linear OOA(49²¹, 1921601, F₄₉, 3, 6) (dual of [(1921601, 3), 5764782, 7]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(49²¹, 5764803, F₄₉, 6) (dual of [5764803, 5764782, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(49²¹, 5764805, F₄₉, 6) (dual of [5764805, 5764784, 7]-code), using
      - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(49²¹, 5764801, F₄₉, 6) (dual of [5764801, 5764780, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(49¹⁷, 5764801, F₄₉, 5) (dual of [5764801, 5764784, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (29, 35, 8388602)-net over F₄₉	[i]		Net Defined by OOA