MinT - Information on Result #1017151

Information on Result #1017151

Linear OOA(49²¹, large, F₄₉, 3, 4), using (u,Â u+v)-construction based on

linear OOA(49², 50, F₄₉, 3, 2) (dual of [(50, 3), 148, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;148,49) [i]
linear OOA(49¹⁹, 8388602, F₄₉, 3, 4) (dual of [(8388602, 3), 25165787, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(49¹⁹, large, F₄₉, 2, 4), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(49⁰, s, F₄₉, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
    2. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    3. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    4. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    5. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    6. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    7. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    8. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    9. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    10. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    11. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    12. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    13. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    14. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    15. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    16. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    17. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    18. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    19. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    20. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    21. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    22. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    23. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    24. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    25. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    26. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    27. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    28. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    29. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    30. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    31. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    32. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    33. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    34. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    35. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    36. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    37. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    38. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    39. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    40. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    41. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    42. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    43. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    44. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    45. linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
    46. linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(49¹, s, F₄₉, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [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]
    47. linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code) (see above)
    48. 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]
    49. linear OOA(49¹³, 2882402, F₄₉, 2, 4) (dual of [(2882402, 2), 5764791, 5]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(49¹³, 5764804, F₄₉, 4) (dual of [5764804, 5764791, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹³, 5764805, F₄₉, 4) (dual of [5764805, 5764792, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(49⁹, 5764801, F₄₉, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(49²¹, large, F₄₉, 3, 3)	[i]		Strength Reduction for OOAs