MinT - Information on Result #2518467

Information on Result #2518467

Linear OOA(27⁵¹, large, F₂₇, 2, 4), using 14 times NRT-code embedding in larger space based on linear OOA(27²³, large, F₂₇, 2, 4), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
3. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
4. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
5. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
6. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
7. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
8. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
9. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
10. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
11. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
12. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
13. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
14. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
15. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
16. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
17. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
18. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
19. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
20. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
21. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
22. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
23. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
24. linear OOA(27¹, 551881, F₂₇, 2, 1) (dual of [(551881, 2), 1103761, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
25. linear OOA(27¹, 551881, F₂₇, 2, 1) (dual of [(551881, 2), 1103761, 2]-NRT-code) (see above)
26. linear OOA(27⁵, 551881, F₂₇, 2, 2) (dual of [(551881, 2), 1103757, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(27⁵, 551881, F₂₇, 2) (dual of [551881, 551876, 3]-code), using
    - Hamming code H(5,27) [i]
27. linear OOA(27¹⁶, 4194301, F₂₇, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27¹⁶, 8388602, F₂₇, 4) (dual of [8388602, 8388586, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(27¹⁶, large, F₂₇, 4) (dual of [large, large−16, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(27⁵², large, F₂₇, 2, 4)	[i]		OOA Duplication