Information on Result #699732
Linear OA(12823, 2097159, F128, 8) (dual of [2097159, 2097136, 9]-code), using construction X applied to Ce(7) ⊂ Ce(5) based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 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 | OA(1641, 2097159, S16, 8) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3233, 2097159, S32, 8) | [i] | ||
| 3 | OA(6427, 2097159, S64, 8) | [i] | ||
| 4 | Linear OOA(12823, 1255608, F128, 2, 8) (dual of [(1255608, 2), 2511193, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12823, 1255608, F128, 3, 8) (dual of [(1255608, 3), 3766801, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(12823, 1255608, F128, 4, 8) (dual of [(1255608, 4), 5022409, 9]-NRT-code) | [i] | ||
| 7 | Digital (15, 23, 1255608)-net over F128 | [i] | ||
| 8 | Linear OOA(12823, 1048579, F128, 2, 8) (dual of [(1048579, 2), 2097135, 9]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12823, 699053, F128, 3, 8) (dual of [(699053, 3), 2097136, 9]-NRT-code) | [i] | ||
| 10 | Linear OOA(12823, 524289, F128, 4, 8) (dual of [(524289, 4), 2097133, 9]-NRT-code) | [i] | ||
| 11 | Linear OOA(12823, 524289, F128, 8, 8) (dual of [(524289, 8), 4194289, 9]-NRT-code) | [i] | OA Folding and Stacking | |