Information on Result #733368
Linear OA(2784, 19872, F27, 22) (dual of [19872, 19788, 23]-code), using (u, u+v)-construction based on
- linear OA(2720, 186, F27, 11) (dual of [186, 166, 12]-code), using
- construction XX applied to C1 = C([181,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([181,9]) [i] based on
- linear OA(2718, 182, F27, 10) (dual of [182, 164, 11]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2718, 182, F27, 10) (dual of [182, 164, 11]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2720, 182, F27, 11) (dual of [182, 162, 12]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2716, 182, F27, 9) (dual of [182, 166, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([181,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([181,9]) [i] based on
- linear OA(2764, 19686, F27, 22) (dual of [19686, 19622, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2761, 19683, F27, 21) (dual of [19683, 19622, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
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(2784, 9936, F27, 2, 22) (dual of [(9936, 2), 19788, 23]-NRT-code) | [i] | OOA Folding | |