Information on Result #733014

Linear OA(2712, 19764, F27, 4) (dual of [19764, 19752, 5]-code), using generalized (u, u+v)-construction based on
  1. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code), using
  2. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  3. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  4. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  5. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  6. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  7. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  8. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  9. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  10. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  11. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  12. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  13. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  14. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  15. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  16. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  17. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  18. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  19. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  20. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  21. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  22. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  23. linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
  24. linear OA(271, 732, F27, 1) (dual of [732, 731, 2]-code), using
  25. linear OA(271, 732, F27, 1) (dual of [732, 731, 2]-code) (see above)
  26. linear OA(273, 732, F27, 2) (dual of [732, 729, 3]-code), using
  27. linear OA(277, 732, F27, 4) (dual of [732, 725, 5]-code), using
    • construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
      1. linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
      2. linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(277, 728, F27, 4) (dual of [728, 721, 5]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
      4. linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(2712, 9882, F27, 2, 4) (dual of [(9882, 2), 19752, 5]-NRT-code) [i]OOA Folding
2Linear OOA(2712, 9882, F27, 4, 4) (dual of [(9882, 4), 39516, 5]-NRT-code) [i]OA Folding and Stacking