Information on Result #806542
Linear OOA(299, 273, F2, 2, 21) (dual of [(273, 2), 447, 22]-NRT-code), using OOA 2-folding based on linear OA(299, 546, F2, 21) (dual of [546, 447, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(299, 547, F2, 21) (dual of [547, 448, 22]-code), using
- adding a parity check bit [i] based on linear OA(298, 546, F2, 20) (dual of [546, 448, 21]-code), using
- construction XX applied to C1 = C([507,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([507,16]) [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 = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(272, 511, F2, 16) (dual of [511, 439, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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 = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(263, 511, F2, 14) (dual of [511, 448, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-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(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
- construction XX applied to C1 = C([507,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([507,16]) [i] based on
- adding a parity check bit [i] based on linear OA(298, 546, F2, 20) (dual of [546, 448, 21]-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 OOA(299, 273, F2, 2, 20) (dual of [(273, 2), 447, 21]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(299, 273, F2, 3, 21) (dual of [(273, 3), 720, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(299, 273, F2, 4, 21) (dual of [(273, 4), 993, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(299, 273, F2, 5, 21) (dual of [(273, 5), 1266, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(299, 273, F2, 6, 21) (dual of [(273, 6), 1539, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(299, 273, F2, 7, 21) (dual of [(273, 7), 1812, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(299, 273, F2, 8, 21) (dual of [(273, 8), 2085, 22]-NRT-code) | [i] | ||
| 8 | Digital (78, 99, 273)-net over F2 | [i] | ||