Information on Result #672381
Linear OA(2152, 262188, F2, 17) (dual of [262188, 262036, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
- linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2109, 262145, F2, 13) (dual of [262145, 262036, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(2151, 262187, F2, 16) (dual of [262187, 262036, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(2152, 131094, F2, 2, 17) (dual of [(131094, 2), 262036, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2152, 87396, F2, 3, 17) (dual of [(87396, 3), 262036, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2152, 65547, F2, 4, 17) (dual of [(65547, 4), 262036, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(2152, 52437, F2, 5, 17) (dual of [(52437, 5), 262033, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(2152, 43698, F2, 6, 17) (dual of [(43698, 6), 262036, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(2152, 37455, F2, 7, 17) (dual of [(37455, 7), 262033, 18]-NRT-code) | [i] | ||
| 8 | Linear OOA(2152, 32773, F2, 8, 17) (dual of [(32773, 8), 262032, 18]-NRT-code) | [i] | ||
| 9 | Linear OOA(2152, 32773, F2, 17, 17) (dual of [(32773, 17), 556989, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |