Information on Result #806099
Linear OOA(268, 137, F2, 2, 17) (dual of [(137, 2), 206, 18]-NRT-code), using OOA 2-folding based on linear OA(268, 274, F2, 17) (dual of [274, 206, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(268, 275, F2, 17) (dual of [275, 207, 18]-code), using
- adding a parity check bit [i] based on linear OA(267, 274, F2, 16) (dual of [274, 207, 17]-code), using
- construction XX applied to C1 = C([253,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([253,14]) [i] based on
- linear OA(257, 255, F2, 15) (dual of [255, 198, 16]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(256, 255, F2, 14) (dual of [255, 199, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(265, 255, F2, 17) (dual of [255, 190, 18]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(248, 255, F2, 12) (dual of [255, 207, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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, 9, F2, 1) (dual of [9, 8, 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([253,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([253,14]) [i] based on
- adding a parity check bit [i] based on linear OA(267, 274, F2, 16) (dual of [274, 207, 17]-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(268, 137, F2, 2, 16) (dual of [(137, 2), 206, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(268, 137, F2, 3, 17) (dual of [(137, 3), 343, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(268, 137, F2, 4, 17) (dual of [(137, 4), 480, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(268, 137, F2, 5, 17) (dual of [(137, 5), 617, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(268, 137, F2, 6, 17) (dual of [(137, 6), 754, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(268, 137, F2, 7, 17) (dual of [(137, 7), 891, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(268, 137, F2, 8, 17) (dual of [(137, 8), 1028, 18]-NRT-code) | [i] | ||
| 8 | Digital (51, 68, 137)-net over F2 | [i] | ||