Information on Result #2259620
Linear OA(2249, 65576, F2, 31) (dual of [65576, 65327, 32]-code), using 1 times code embedding in larger space based on linear OA(2248, 65575, F2, 31) (dual of [65575, 65327, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(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 OOA(2249, 32788, F2, 2, 31) (dual of [(32788, 2), 65327, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2249, 16394, F2, 4, 31) (dual of [(16394, 4), 65327, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2249, 9368, F2, 7, 31) (dual of [(9368, 7), 65327, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2249, 8197, F2, 8, 31) (dual of [(8197, 8), 65327, 32]-NRT-code) | [i] | ||