Information on Result #805921
Linear OOA(259, 136, F2, 2, 15) (dual of [(136, 2), 213, 16]-NRT-code), using OOA 2-folding based on linear OA(259, 272, F2, 15) (dual of [272, 213, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(259, 273, F2, 15) (dual of [273, 214, 16]-code), using
- construction XX applied to C1 = C([253,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([253,12]) [i] based on
- linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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, using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
- construction XX applied to C1 = C([253,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([253,12]) [i] based on
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, 126, F2, 3, 15) (dual of [(126, 3), 319, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(259, 126, F2, 4, 15) (dual of [(126, 4), 445, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(259, 126, F2, 5, 15) (dual of [(126, 5), 571, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(259, 126, F2, 6, 15) (dual of [(126, 6), 697, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(259, 126, F2, 7, 15) (dual of [(126, 7), 823, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(259, 126, F2, 8, 15) (dual of [(126, 8), 949, 16]-NRT-code) | [i] | ||
| 7 | Digital (44, 59, 126)-net over F2 | [i] | ||