Information on Result #2226891
Linear OA(2215, 65574, F2, 26) (dual of [65574, 65359, 27]-code), using 1 times truncation based on linear OA(2216, 65575, F2, 27) (dual of [65575, 65359, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-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(2217, 65576, F2, 26) (dual of [65576, 65359, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2218, 65577, F2, 26) (dual of [65577, 65359, 27]-code) | [i] | ||
| 3 | Linear OA(2219, 65578, F2, 26) (dual of [65578, 65359, 27]-code) | [i] | ||
| 4 | Linear OOA(2215, 32787, F2, 2, 26) (dual of [(32787, 2), 65359, 27]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2215, 21858, F2, 3, 26) (dual of [(21858, 3), 65359, 27]-NRT-code) | [i] | ||
| 6 | Linear OOA(2215, 16393, F2, 4, 26) (dual of [(16393, 4), 65357, 27]-NRT-code) | [i] | ||
| 7 | Linear OOA(2215, 13114, F2, 5, 26) (dual of [(13114, 5), 65355, 27]-NRT-code) | [i] | ||
| 8 | Linear OOA(2215, 10929, F2, 6, 26) (dual of [(10929, 6), 65359, 27]-NRT-code) | [i] | ||
| 9 | Linear OOA(2215, 9367, F2, 7, 26) (dual of [(9367, 7), 65354, 27]-NRT-code) | [i] | ||
| 10 | Linear OOA(2215, 8196, F2, 8, 26) (dual of [(8196, 8), 65353, 27]-NRT-code) | [i] | ||
| 11 | Linear OOA(2215, 5044, F2, 26, 26) (dual of [(5044, 26), 130929, 27]-NRT-code) | [i] | OA Folding and Stacking | |