Information on Result #672371
Linear OA(2224, 262188, F2, 25) (dual of [262188, 261964, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(2217, 262145, F2, 25) (dual of [262145, 261928, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2181, 262145, F2, 21) (dual of [262145, 261964, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 43, F2, 3) (dual of [43, 36, 4]-code or 43-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(2224, 262188, F2, 24) (dual of [262188, 261964, 25]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2225, 262189, F2, 25) (dual of [262189, 261964, 26]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2226, 262190, F2, 25) (dual of [262190, 261964, 26]-code) | [i] | ||
| 4 | Linear OA(2227, 262191, F2, 25) (dual of [262191, 261964, 26]-code) | [i] | ||
| 5 | Linear OA(2228, 262192, F2, 25) (dual of [262192, 261964, 26]-code) | [i] | ||
| 6 | Linear OA(2223, 262187, F2, 24) (dual of [262187, 261964, 25]-code) | [i] | Truncation | |
| 7 | Linear OOA(2224, 131094, F2, 2, 25) (dual of [(131094, 2), 261964, 26]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2224, 87396, F2, 3, 25) (dual of [(87396, 3), 261964, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2224, 65547, F2, 4, 25) (dual of [(65547, 4), 261964, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(2224, 52437, F2, 5, 25) (dual of [(52437, 5), 261961, 26]-NRT-code) | [i] | ||
| 11 | Linear OOA(2224, 43698, F2, 6, 25) (dual of [(43698, 6), 261964, 26]-NRT-code) | [i] | ||
| 12 | Linear OOA(2224, 37455, F2, 7, 25) (dual of [(37455, 7), 261961, 26]-NRT-code) | [i] | ||
| 13 | Linear OOA(2224, 32773, F2, 8, 25) (dual of [(32773, 8), 261960, 26]-NRT-code) | [i] | ||