Information on Result #731917
Linear OA(9143, 59138, F9, 27) (dual of [59138, 58995, 28]-code), using (u, u+v)-construction based on
- linear OA(922, 84, F9, 13) (dual of [84, 62, 14]-code), using
- construction XX applied to C1 = C([79,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([79,11]) [i] based on
- linear OA(920, 80, F9, 12) (dual of [80, 60, 13]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(920, 80, F9, 12) (dual of [80, 60, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(922, 80, F9, 13) (dual of [80, 58, 14]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(918, 80, F9, 11) (dual of [80, 62, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([79,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([79,11]) [i] based on
- linear OA(9121, 59054, F9, 27) (dual of [59054, 58933, 28]-code), using
- 1 times truncation [i] based on linear OA(9122, 59055, F9, 28) (dual of [59055, 58933, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(91, 6, F9, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- 1 times truncation [i] based on linear OA(9122, 59055, F9, 28) (dual of [59055, 58933, 29]-code), using
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(9143, 29569, F9, 2, 27) (dual of [(29569, 2), 58995, 28]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(9143, 19712, F9, 3, 27) (dual of [(19712, 3), 58993, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(9143, 4549, F9, 27, 27) (dual of [(4549, 27), 122680, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |