Information on Result #704923
Linear OA(3169, 785, F3, 39) (dual of [785, 616, 40]-code), using construction XX applied to C1 = C([722,28]), C2 = C([0,33]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([722,33]) based on
- linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,28}, and designed minimum distance d ≥ |I|+1 = 36 [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(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(38, 32, F3, 4) (dual of [32, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-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(3169, 392, F3, 2, 39) (dual of [(392, 2), 615, 40]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3169, 261, F3, 3, 39) (dual of [(261, 3), 614, 40]-NRT-code) | [i] | ||