Information on Result #732185

Linear OA(2512, 15700, F25, 4) (dual of [15700, 15688, 5]-code), using generalized (u, u+v)-construction based on
  1. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code), using
  2. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  3. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  4. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  5. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  6. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  7. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  8. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  9. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  10. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  11. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  12. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  13. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  14. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  15. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  16. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  17. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  18. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  19. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  20. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  21. linear OA(250, 628, F25, 0) (dual of [628, 628, 1]-code) (see above)
  22. linear OA(251, 628, F25, 1) (dual of [628, 627, 2]-code), using
  23. linear OA(251, 628, F25, 1) (dual of [628, 627, 2]-code) (see above)
  24. linear OA(253, 628, F25, 2) (dual of [628, 625, 3]-code), using
  25. linear OA(257, 628, F25, 4) (dual of [628, 621, 5]-code), using
    • construction XX applied to C1 = C([623,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([623,2]) [i] based on
      1. linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
      2. linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
      4. linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
      5. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(250, 2, F25, 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(2512, 7850, F25, 2, 4) (dual of [(7850, 2), 15688, 5]-NRT-code) [i]OOA Folding
2Linear OOA(2512, 7850, F25, 4, 4) (dual of [(7850, 4), 31388, 5]-NRT-code) [i]OA Folding and Stacking