Information on Result #2220422
Linear OA(262, 279, F2, 14) (dual of [279, 217, 15]-code), using 1 times truncation based on linear OA(263, 280, F2, 15) (dual of [280, 217, 16]-code), using
- construction XX applied to C1 = C([251,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([251,10]) [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 = {−4,−3,…,8}, and designed minimum distance d ≥ |I|+1 = 14 [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(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 = {−4,−3,…,10}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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, 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(262, 165, F2, 2, 14) (dual of [(165, 2), 268, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(262, 165, F2, 3, 14) (dual of [(165, 3), 433, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(262, 165, F2, 4, 14) (dual of [(165, 4), 598, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(262, 165, F2, 5, 14) (dual of [(165, 5), 763, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(262, 165, F2, 6, 14) (dual of [(165, 6), 928, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(262, 165, F2, 7, 14) (dual of [(165, 7), 1093, 15]-NRT-code) | [i] | ||
| 7 | Linear OOA(262, 165, F2, 8, 14) (dual of [(165, 8), 1258, 15]-NRT-code) | [i] | ||
| 8 | Digital (48, 62, 165)-net over F2 | [i] | ||
| 9 | Linear OOA(262, 139, F2, 2, 14) (dual of [(139, 2), 216, 15]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(262, 93, F2, 3, 14) (dual of [(93, 3), 217, 15]-NRT-code) | [i] | ||