Information on Result #673346
Linear OA(2226, 557, F2, 51) (dual of [557, 331, 52]-code), using construction X applied to Ce(50) ⊂ Ce(42) based on
- linear OA(2208, 512, F2, 51) (dual of [512, 304, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2181, 512, F2, 43) (dual of [512, 331, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(218, 45, F2, 7) (dual of [45, 27, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(218, 48, F2, 7) (dual of [48, 30, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- extended Golay code Ge(2) [i]
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(218, 48, F2, 7) (dual of [48, 30, 8]-code), 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(2226, 557, F2, 50) (dual of [557, 331, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2227, 558, F2, 51) (dual of [558, 331, 52]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2228, 559, F2, 51) (dual of [559, 331, 52]-code) | [i] | ||
| 4 | Linear OA(2229, 560, F2, 51) (dual of [560, 331, 52]-code) | [i] | ||
| 5 | Linear OA(2230, 561, F2, 51) (dual of [561, 331, 52]-code) | [i] | ||
| 6 | Linear OA(2225, 556, F2, 50) (dual of [556, 331, 51]-code) | [i] | Truncation | |
| 7 | Linear OOA(2226, 278, F2, 2, 51) (dual of [(278, 2), 330, 52]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2226, 139, F2, 4, 51) (dual of [(139, 4), 330, 52]-NRT-code) | [i] | ||