Information on Result #806747
Linear OOA(289, 138, F2, 2, 23) (dual of [(138, 2), 187, 24]-NRT-code), using OOA 2-folding based on linear OA(289, 276, F2, 23) (dual of [276, 187, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(288, 275, F2, 23) (dual of [275, 187, 24]-code), using
- adding a parity check bit [i] based on linear OA(287, 274, F2, 22) (dual of [274, 187, 23]-code), using
- construction XX applied to C1 = C([253,18]), C2 = C([1,20]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([253,20]) [i] based on
- linear OA(277, 255, F2, 21) (dual of [255, 178, 22]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(276, 255, F2, 20) (dual of [255, 179, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,20}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(268, 255, F2, 18) (dual of [255, 187, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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([253,18]), C2 = C([1,20]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([253,20]) [i] based on
- adding a parity check bit [i] based on linear OA(287, 274, F2, 22) (dual of [274, 187, 23]-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(289, 138, F2, 2, 22) (dual of [(138, 2), 187, 23]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(289, 138, F2, 3, 23) (dual of [(138, 3), 325, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(289, 138, F2, 4, 23) (dual of [(138, 4), 463, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(289, 138, F2, 5, 23) (dual of [(138, 5), 601, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(289, 138, F2, 6, 23) (dual of [(138, 6), 739, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(289, 138, F2, 7, 23) (dual of [(138, 7), 877, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(289, 138, F2, 8, 23) (dual of [(138, 8), 1015, 24]-NRT-code) | [i] | ||
| 8 | Digital (66, 89, 138)-net over F2 | [i] | ||