Information on Result #704934
Linear OA(3163, 769, F3, 39) (dual of [769, 606, 40]-code), using construction XX applied to C1 = C([722,30]), C2 = C([0,33]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([722,33]) based on
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3130, 728, F3, 34) (dual of [728, 598, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3154, 728, F3, 40) (dual of [728, 574, 41]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,33}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
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 OA(3164, 770, F3, 39) (dual of [770, 606, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3163, 384, F3, 2, 39) (dual of [(384, 2), 605, 40]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3163, 256, F3, 3, 39) (dual of [(256, 3), 605, 40]-NRT-code) | [i] | ||