Information on Result #672416
Linear OA(2242, 262187, F2, 27) (dual of [262187, 261945, 28]-code), using construction X applied to Ce(26) ⊂ Ce(22) based on
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2199, 262144, F2, 23) (dual of [262144, 261945, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(2242, 262187, F2, 26) (dual of [262187, 261945, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2243, 262188, F2, 27) (dual of [262188, 261945, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2244, 262189, F2, 27) (dual of [262189, 261945, 28]-code) | [i] | ||
| 4 | Linear OA(2245, 262190, F2, 27) (dual of [262190, 261945, 28]-code) | [i] | ||
| 5 | Linear OA(2246, 262191, F2, 27) (dual of [262191, 261945, 28]-code) | [i] | ||
| 6 | Linear OA(2247, 262192, F2, 27) (dual of [262192, 261945, 28]-code) | [i] | ||
| 7 | Linear OA(2241, 262186, F2, 26) (dual of [262186, 261945, 27]-code) | [i] | Truncation | |
| 8 | Linear OOA(2242, 131093, F2, 2, 27) (dual of [(131093, 2), 261944, 28]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(2242, 87395, F2, 3, 27) (dual of [(87395, 3), 261943, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(2242, 65546, F2, 4, 27) (dual of [(65546, 4), 261942, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(2242, 52437, F2, 5, 27) (dual of [(52437, 5), 261943, 28]-NRT-code) | [i] | ||
| 12 | Linear OOA(2242, 43697, F2, 6, 27) (dual of [(43697, 6), 261940, 28]-NRT-code) | [i] | ||
| 13 | Linear OOA(2242, 37455, F2, 7, 27) (dual of [(37455, 7), 261943, 28]-NRT-code) | [i] | ||
| 14 | Linear OOA(2242, 32773, F2, 8, 27) (dual of [(32773, 8), 261942, 28]-NRT-code) | [i] | ||
| 15 | Linear OOA(2242, 20168, F2, 27, 27) (dual of [(20168, 27), 544294, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |