Information on Result #805778
Linear OOA(253, 138, F2, 2, 13) (dual of [(138, 2), 223, 14]-NRT-code), using OOA 2-folding based on linear OA(253, 276, F2, 13) (dual of [276, 223, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(252, 275, F2, 13) (dual of [275, 223, 14]-code), using
- adding a parity check bit [i] based on linear OA(251, 274, F2, 12) (dual of [274, 223, 13]-code), using
- construction XX applied to C1 = C([253,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([253,10]) [i] based on
- 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(240, 255, F2, 10) (dual of [255, 215, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(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(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([253,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([253,10]) [i] based on
- adding a parity check bit [i] based on linear OA(251, 274, F2, 12) (dual of [274, 223, 13]-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(253, 138, F2, 2, 12) (dual of [(138, 2), 223, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(254, 138, F2, 2, 13) (dual of [(138, 2), 222, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(253, 138, F2, 3, 13) (dual of [(138, 3), 361, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(253, 138, F2, 4, 13) (dual of [(138, 4), 499, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(253, 138, F2, 5, 13) (dual of [(138, 5), 637, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(253, 138, F2, 6, 13) (dual of [(138, 6), 775, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(253, 138, F2, 7, 13) (dual of [(138, 7), 913, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(253, 138, F2, 8, 13) (dual of [(138, 8), 1051, 14]-NRT-code) | [i] | ||
| 9 | Digital (40, 53, 138)-net over F2 | [i] | ||