Information on Result #704161
Linear OA(345, 743, F3, 11) (dual of [743, 698, 12]-code), using construction XX applied to C1 = C([727,7]), C2 = C([1,9]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([727,9]) based on
- linear OA(337, 728, F3, 9) (dual of [728, 691, 10]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(336, 728, F3, 9) (dual of [728, 692, 10]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(343, 728, F3, 11) (dual of [728, 685, 12]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(330, 728, F3, 7) (dual of [728, 698, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(31, 8, F3, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(345, 371, F3, 2, 11) (dual of [(371, 2), 697, 12]-NRT-code) | [i] | OOA Folding | |