Information on Result #2417087
Linear OOA(259, 267, F2, 2, 12) (dual of [(267, 2), 475, 13]-NRT-code), using strength reduction based on linear OOA(259, 267, F2, 2, 13) (dual of [(267, 2), 475, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(259, 534, F2, 13) (dual of [534, 475, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(258, 533, F2, 13) (dual of [533, 475, 14]-code), using
- adding a parity check bit [i] based on linear OA(257, 532, F2, 12) (dual of [532, 475, 13]-code), using
- construction XX applied to C1 = C([509,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([509,10]) [i] based on
- linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(245, 511, F2, 10) (dual of [511, 466, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(255, 511, F2, 13) (dual of [511, 456, 14]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(236, 511, F2, 8) (dual of [511, 475, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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([509,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([509,10]) [i] based on
- adding a parity check bit [i] based on linear OA(257, 532, F2, 12) (dual of [532, 475, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(258, 533, F2, 13) (dual of [533, 475, 14]-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(259, 267, F2, 3, 12) (dual of [(267, 3), 742, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(259, 267, F2, 4, 12) (dual of [(267, 4), 1009, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(259, 267, F2, 5, 12) (dual of [(267, 5), 1276, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(259, 267, F2, 6, 12) (dual of [(267, 6), 1543, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(259, 267, F2, 7, 12) (dual of [(267, 7), 1810, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(259, 267, F2, 8, 12) (dual of [(267, 8), 2077, 13]-NRT-code) | [i] | ||
| 7 | Digital (47, 59, 267)-net over F2 | [i] | ||