MinT - Information on Result #2520315

Information on Result #2520315

Linear OOA(49³⁵, large, F₄₉, 2, 3), using 49¹ times duplication based on linear OOA(49³⁴, large, F₄₉, 2, 3), using

strength reduction [i] based on linear OOA(49³⁴, large, F₄₉, 2, 6), 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(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]
  45. linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code) (see above)
  46. linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code) (see above)
  47. 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(49⁶, 120200, F₄₉, 2, 3) (dual of [(120200, 2), 240394, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(49⁶, 120200, F₄₉, 3) (dual of [120200, 120194, 4]-code or 120200-cap in PG(5,49)), using
      - large caps in PG(5,Â b) [i]
  49. linear OOA(49²¹, 2882402, F₄₉, 2, 6) (dual of [(2882402, 2), 5764783, 7]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(49²¹, 5764804, F₄₉, 6) (dual of [5764804, 5764783, 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.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.