Information on Result #2478872
Linear OOA(297, 268, F2, 2, 21) (dual of [(268, 2), 439, 22]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(295, 267, F2, 2, 21) (dual of [(267, 2), 439, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(295, 534, F2, 21) (dual of [534, 439, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(294, 533, F2, 21) (dual of [533, 439, 22]-code), using
- adding a parity check bit [i] based on linear OA(293, 532, F2, 20) (dual of [532, 439, 21]-code), using
- construction XX applied to C1 = C([509,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), 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(281, 511, F2, 18) (dual of [511, 430, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(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(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([509,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([509,18]) [i] based on
- adding a parity check bit [i] based on linear OA(293, 532, F2, 20) (dual of [532, 439, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(294, 533, F2, 21) (dual of [533, 439, 22]-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(297, 268, F2, 3, 21) (dual of [(268, 3), 707, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(297, 268, F2, 4, 21) (dual of [(268, 4), 975, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(297, 268, F2, 5, 21) (dual of [(268, 5), 1243, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(297, 268, F2, 6, 21) (dual of [(268, 6), 1511, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(297, 268, F2, 7, 21) (dual of [(268, 7), 1779, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(297, 268, F2, 8, 21) (dual of [(268, 8), 2047, 22]-NRT-code) | [i] | ||
| 7 | Digital (76, 97, 268)-net over F2 | [i] | ||