Information on Result #703086
Linear OA(321, 252, F3, 6) (dual of [252, 231, 7]-code), using construction XX applied to C1 = C([241,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([241,4]) based on
- linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(321, 242, F3, 6) (dual of [242, 221, 7]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(311, 242, F3, 4) (dual of [242, 231, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- 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
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code) (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(321, 252, F3, 2, 6) (dual of [(252, 2), 483, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(321, 252, F3, 3, 6) (dual of [(252, 3), 735, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(321, 252, F3, 4, 6) (dual of [(252, 4), 987, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(321, 252, F3, 5, 6) (dual of [(252, 5), 1239, 7]-NRT-code) | [i] | ||
| 5 | Linear OA(322, 256, F3, 6) (dual of [256, 234, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(323, 267, F3, 6) (dual of [267, 244, 7]-code) | [i] | ||
| 7 | Linear OOA(321, 126, F3, 2, 6) (dual of [(126, 2), 231, 7]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(321, 84, F3, 3, 6) (dual of [(84, 3), 231, 7]-NRT-code) | [i] | ||