Information on Result #805523
Linear OOA(236, 137, F2, 2, 9) (dual of [(137, 2), 238, 10]-NRT-code), using OOA 2-folding based on linear OA(236, 274, F2, 9) (dual of [274, 238, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(236, 275, F2, 9) (dual of [275, 239, 10]-code), using
- adding a parity check bit [i] based on linear OA(235, 274, F2, 8) (dual of [274, 239, 9]-code), using
- construction XX applied to C1 = C([253,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(224, 255, F2, 6) (dual of [255, 231, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(216, 255, F2, 4) (dual of [255, 239, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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([253,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- adding a parity check bit [i] based on linear OA(235, 274, F2, 8) (dual of [274, 239, 9]-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(2243, 4194438, F2, 2, 18) (dual of [(4194438, 2), 8388633, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2244, 4194438, F2, 2, 19) (dual of [(4194438, 2), 8388632, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(236, 137, F2, 3, 9) (dual of [(137, 3), 375, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(236, 137, F2, 4, 9) (dual of [(137, 4), 512, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(236, 137, F2, 5, 9) (dual of [(137, 5), 649, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(236, 137, F2, 6, 9) (dual of [(137, 6), 786, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(236, 137, F2, 7, 9) (dual of [(137, 7), 923, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(236, 137, F2, 8, 9) (dual of [(137, 8), 1060, 10]-NRT-code) | [i] | ||