Information on Result #1304089
Linear OA(326, 745, F3, 6) (dual of [745, 719, 7]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(325, 740, F3, 6) (dual of [740, 715, 7]-code), using
- construction XX applied to C1 = C([727,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([727,4]) [i] based on
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(325, 728, F3, 6) (dual of [728, 703, 7]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(313, 728, F3, 4) (dual of [728, 715, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code) (see above)
Mode: 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(326, 745, F3, 2, 6) (dual of [(745, 2), 1464, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(326, 745, F3, 3, 6) (dual of [(745, 3), 2209, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(326, 745, F3, 4, 6) (dual of [(745, 4), 2954, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(326, 745, F3, 5, 6) (dual of [(745, 5), 3699, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(326, 372, F3, 2, 6) (dual of [(372, 2), 718, 7]-NRT-code) | [i] | OOA Folding | |