Information on Result #1509192
Linear OOA(240, 234, F2, 3, 9) (dual of [(234, 3), 662, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(240, 234, F2, 2, 9) (dual of [(234, 2), 428, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 266, F2, 2, 9) (dual of [(266, 2), 492, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(240, 532, F2, 9) (dual of [532, 492, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(240, 533, F2, 9) (dual of [533, 493, 10]-code), using
- adding a parity check bit [i] based on linear OA(239, 532, F2, 8) (dual of [532, 493, 9]-code), using
- construction XX applied to C1 = C([509,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- linear OA(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(227, 511, F2, 6) (dual of [511, 484, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(237, 511, F2, 9) (dual of [511, 474, 10]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(218, 511, F2, 4) (dual of [511, 493, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to C1 = C([509,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- adding a parity check bit [i] based on linear OA(239, 532, F2, 8) (dual of [532, 493, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(240, 533, F2, 9) (dual of [533, 493, 10]-code), using
- OOA 2-folding [i] based on linear OA(240, 532, F2, 9) (dual of [532, 492, 10]-code), using
Mode: 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(2247, 2796435, F2, 3, 18) (dual of [(2796435, 3), 8389058, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2248, 2796435, F2, 3, 19) (dual of [(2796435, 3), 8389057, 20]-NRT-code) | [i] | ||