Information on Result #672563
Linear OA(2218, 32806, F2, 29) (dual of [32806, 32588, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,12]) based on
- linear OA(2211, 32769, F2, 29) (dual of [32769, 32558, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2181, 32769, F2, 25) (dual of [32769, 32588, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(27, 37, F2, 3) (dual of [37, 30, 4]-code or 37-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(2218, 32806, F2, 28) (dual of [32806, 32588, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2219, 32807, F2, 29) (dual of [32807, 32588, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2220, 32808, F2, 29) (dual of [32808, 32588, 30]-code) | [i] | ||
| 4 | Linear OA(2221, 32809, F2, 29) (dual of [32809, 32588, 30]-code) | [i] | ||
| 5 | Linear OA(2222, 32810, F2, 29) (dual of [32810, 32588, 30]-code) | [i] | ||
| 6 | Linear OA(2217, 32805, F2, 28) (dual of [32805, 32588, 29]-code) | [i] | Truncation | |
| 7 | Linear OOA(2218, 16403, F2, 2, 29) (dual of [(16403, 2), 32588, 30]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2218, 10935, F2, 3, 29) (dual of [(10935, 3), 32587, 30]-NRT-code) | [i] | ||
| 9 | Linear OOA(2218, 8201, F2, 4, 29) (dual of [(8201, 4), 32586, 30]-NRT-code) | [i] | ||
| 10 | Linear OOA(2218, 6561, F2, 5, 29) (dual of [(6561, 5), 32587, 30]-NRT-code) | [i] | ||
| 11 | Linear OOA(2218, 5467, F2, 6, 29) (dual of [(5467, 6), 32584, 30]-NRT-code) | [i] | ||
| 12 | Linear OOA(2218, 4686, F2, 7, 29) (dual of [(4686, 7), 32584, 30]-NRT-code) | [i] | ||
| 13 | Linear OOA(2218, 2343, F2, 29, 29) (dual of [(2343, 29), 67729, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |