Information on Result #672573
Linear OA(2158, 32806, F2, 21) (dual of [32806, 32648, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2151, 32769, F2, 21) (dual of [32769, 32618, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2121, 32769, F2, 17) (dual of [32769, 32648, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(2158, 32806, F2, 20) (dual of [32806, 32648, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2159, 32807, F2, 21) (dual of [32807, 32648, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2160, 32808, F2, 21) (dual of [32808, 32648, 22]-code) | [i] | ||
| 4 | Linear OA(2157, 32805, F2, 20) (dual of [32805, 32648, 21]-code) | [i] | Truncation | |
| 5 | Linear OOA(2158, 16403, F2, 2, 21) (dual of [(16403, 2), 32648, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2158, 10935, F2, 3, 21) (dual of [(10935, 3), 32647, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2158, 8201, F2, 4, 21) (dual of [(8201, 4), 32646, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2158, 6561, F2, 5, 21) (dual of [(6561, 5), 32647, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2158, 5467, F2, 6, 21) (dual of [(5467, 6), 32644, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2158, 4686, F2, 7, 21) (dual of [(4686, 7), 32644, 22]-NRT-code) | [i] | ||