Information on Result #2417801
Linear OOA(286, 267, F2, 2, 18) (dual of [(267, 2), 448, 19]-NRT-code), using strength reduction based on linear OOA(286, 267, F2, 2, 19) (dual of [(267, 2), 448, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(286, 534, F2, 19) (dual of [534, 448, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(285, 533, F2, 19) (dual of [533, 448, 20]-code), using
- adding a parity check bit [i] based on linear OA(284, 532, F2, 18) (dual of [532, 448, 19]-code), using
- construction XX applied to C1 = C([509,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([509,16]) [i] based on
- linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [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(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(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(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([509,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([509,16]) [i] based on
- adding a parity check bit [i] based on linear OA(284, 532, F2, 18) (dual of [532, 448, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(285, 533, F2, 19) (dual of [533, 448, 20]-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(286, 267, F2, 3, 18) (dual of [(267, 3), 715, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(286, 267, F2, 4, 18) (dual of [(267, 4), 982, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(286, 267, F2, 5, 18) (dual of [(267, 5), 1249, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(286, 267, F2, 6, 18) (dual of [(267, 6), 1516, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(286, 267, F2, 7, 18) (dual of [(267, 7), 1783, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(286, 267, F2, 8, 18) (dual of [(267, 8), 2050, 19]-NRT-code) | [i] | ||
| 7 | Digital (68, 86, 267)-net over F2 | [i] | ||