Information on Result #703573
Linear OA(3128, 264, F3, 41) (dual of [264, 136, 42]-code), using construction XX applied to C1 = C([82,121]), C2 = C([87,122]), C3 = C1 + C2 = C([87,121]), and C∩ = C1 ∩ C2 = C([82,122]) based on
- linear OA(3116, 242, F3, 40) (dual of [242, 126, 41]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {82,83,…,121}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3111, 242, F3, 36) (dual of [242, 131, 37]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {87,88,…,122}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3121, 242, F3, 41) (dual of [242, 121, 42]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {82,83,…,122}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3106, 242, F3, 35) (dual of [242, 136, 36]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {87,88,…,121}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(37, 17, F3, 4) (dual of [17, 10, 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
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-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 OOA(3128, 132, F3, 2, 41) (dual of [(132, 2), 136, 42]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3128, 88, F3, 3, 41) (dual of [(88, 3), 136, 42]-NRT-code) | [i] | ||