MinT - Information on Result #906747

Information on Result #906747

Linear OOA(25⁷⁰, 4194951, F₂₅, 2, 12) (dual of [(4194951, 2), 8389832, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁴, 650, F₂₅, 2, 6) (dual of [(650, 2), 1286, 7]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁰, s, F₂₅, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  3. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  4. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  5. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  6. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  7. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  8. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  9. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  10. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  11. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  12. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  13. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  14. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  15. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  16. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  17. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  18. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  19. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
  20. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25¹, s, F₂₅, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  21. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
  22. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
  23. linear OOA(25², 26, F₂₅, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;50,25) [i]
  24. linear OOA(25³, 26, F₂₅, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;49,25) [i]
  25. linear OOA(25⁶, 26, F₂₅, 2, 6) (dual of [(26, 2), 46, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;46,25) [i]
linear OOA(25⁵⁶, 4194301, F₂₅, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵⁶, 8388602, F₂₅, 12) (dual of [8388602, 8388546, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, 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(25⁷⁰, 1398316, F₂₅, 14, 12) (dual of [(1398316, 14), 19576354, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row