Information on Result #805526
Linear OOA(239, 265, F2, 2, 9) (dual of [(265, 2), 491, 10]-NRT-code), using OOA 2-folding based on linear OA(239, 530, F2, 9) (dual of [530, 491, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(239, 531, F2, 9) (dual of [531, 492, 10]-code), using
- construction XX applied to C1 = C([509,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), 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(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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(219, 511, F2, 5) (dual of [511, 492, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 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, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([509,6]) [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(2246, 4194566, F2, 2, 18) (dual of [(4194566, 2), 8388886, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2247, 4194566, F2, 2, 19) (dual of [(4194566, 2), 8388885, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(239, 207, F2, 3, 9) (dual of [(207, 3), 582, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(239, 207, F2, 4, 9) (dual of [(207, 4), 789, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(239, 207, F2, 5, 9) (dual of [(207, 5), 996, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(239, 207, F2, 6, 9) (dual of [(207, 6), 1203, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(239, 207, F2, 7, 9) (dual of [(207, 7), 1410, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(239, 207, F2, 8, 9) (dual of [(207, 8), 1617, 10]-NRT-code) | [i] | ||