Information on Result #806538
Linear OOA(293, 265, F2, 2, 21) (dual of [(265, 2), 437, 22]-NRT-code), using OOA 2-folding based on linear OA(293, 530, F2, 21) (dual of [530, 437, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(293, 531, F2, 21) (dual of [531, 438, 22]-code), using
- construction XX applied to C1 = C([509,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([509,18]) [i] based on
- linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(291, 511, F2, 21) (dual of [511, 420, 22]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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([509,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([509,18]) [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(293, 227, F2, 3, 21) (dual of [(227, 3), 588, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(293, 227, F2, 4, 21) (dual of [(227, 4), 815, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(293, 227, F2, 5, 21) (dual of [(227, 5), 1042, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(293, 227, F2, 6, 21) (dual of [(227, 6), 1269, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(293, 227, F2, 7, 21) (dual of [(227, 7), 1496, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(293, 227, F2, 8, 21) (dual of [(227, 8), 1723, 22]-NRT-code) | [i] | ||
| 7 | Digital (72, 93, 227)-net over F2 | [i] | ||