Information on Result #805467
Linear OOA(239, 266, F2, 2, 8) (dual of [(266, 2), 493, 9]-NRT-code), using OOA 2-folding 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)
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(2223, 4194567, F2, 2, 16) (dual of [(4194567, 2), 8388911, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2224, 4194567, F2, 2, 17) (dual of [(4194567, 2), 8388910, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(239, 266, F2, 3, 8) (dual of [(266, 3), 759, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(239, 266, F2, 4, 8) (dual of [(266, 4), 1025, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(239, 266, F2, 5, 8) (dual of [(266, 5), 1291, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(239, 266, F2, 6, 8) (dual of [(266, 6), 1557, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(239, 266, F2, 7, 8) (dual of [(266, 7), 1823, 9]-NRT-code) | [i] | ||