Information on Result #672426
Linear OA(2246, 131114, F2, 29) (dual of [131114, 130868, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,12]) based on
- linear OA(2239, 131073, F2, 29) (dual of [131073, 130834, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2205, 131073, F2, 25) (dual of [131073, 130868, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2246, 131114, F2, 28) (dual of [131114, 130868, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2247, 131115, F2, 29) (dual of [131115, 130868, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2248, 131116, F2, 29) (dual of [131116, 130868, 30]-code) | [i] | ||
| 4 | Linear OA(2249, 131117, F2, 29) (dual of [131117, 130868, 30]-code) | [i] | ||
| 5 | Linear OA(2250, 131118, F2, 29) (dual of [131118, 130868, 30]-code) | [i] | ||
| 6 | Linear OA(2245, 131113, F2, 28) (dual of [131113, 130868, 29]-code) | [i] | Truncation | |
| 7 | Linear OOA(2246, 65557, F2, 2, 29) (dual of [(65557, 2), 130868, 30]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2246, 43704, F2, 3, 29) (dual of [(43704, 3), 130866, 30]-NRT-code) | [i] | ||
| 9 | Linear OOA(2246, 32778, F2, 4, 29) (dual of [(32778, 4), 130866, 30]-NRT-code) | [i] | ||
| 10 | Linear OOA(2246, 26222, F2, 5, 29) (dual of [(26222, 5), 130864, 30]-NRT-code) | [i] | ||
| 11 | Linear OOA(2246, 21852, F2, 6, 29) (dual of [(21852, 6), 130866, 30]-NRT-code) | [i] | ||
| 12 | Linear OOA(2246, 18730, F2, 7, 29) (dual of [(18730, 7), 130864, 30]-NRT-code) | [i] | ||
| 13 | Linear OOA(2246, 16389, F2, 8, 29) (dual of [(16389, 8), 130866, 30]-NRT-code) | [i] | ||
| 14 | Linear OOA(2246, 9365, F2, 29, 29) (dual of [(9365, 29), 271339, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |