Information on Result #1053239
Linear OOA(2258, 131084, F2, 4, 27) (dual of [(131084, 4), 524078, 28]-NRT-code), using OOA 4-folding based on linear OA(2258, 524336, F2, 27) (dual of [524336, 524078, 28]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2255, 524333, F2, 27) (dual of [524333, 524078, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-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
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
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(2258, 131084, F2, 4, 26) (dual of [(131084, 4), 524078, 27]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2259, 131084, F2, 4, 27) (dual of [(131084, 4), 524077, 28]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2260, 131084, F2, 4, 27) (dual of [(131084, 4), 524076, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2257, 131083, F2, 4, 26) (dual of [(131083, 4), 524075, 27]-NRT-code) | [i] | Truncation for OOAs | |