Information on Result #2175604
Linear OA(244, 275, F2, 10) (dual of [275, 231, 11]-code), using strength reduction based on linear OA(244, 275, F2, 11) (dual of [275, 231, 12]-code), using
- adding a parity check bit [i] based on linear OA(243, 274, F2, 10) (dual of [274, 231, 11]-code), using
- construction XX applied to C1 = C([253,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([253,8]) [i] based on
- 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(232, 255, F2, 8) (dual of [255, 223, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [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(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([253,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([253,8]) [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(244, 146, F2, 2, 10) (dual of [(146, 2), 248, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(244, 146, F2, 3, 10) (dual of [(146, 3), 394, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(244, 146, F2, 4, 10) (dual of [(146, 4), 540, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(244, 146, F2, 5, 10) (dual of [(146, 5), 686, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(244, 146, F2, 6, 10) (dual of [(146, 6), 832, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(244, 146, F2, 7, 10) (dual of [(146, 7), 978, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(244, 146, F2, 8, 10) (dual of [(146, 8), 1124, 11]-NRT-code) | [i] | ||
| 8 | Digital (34, 44, 146)-net over F2 | [i] | ||