Information on Result #699802
Linear OA(12846, 2097179, F128, 14) (dual of [2097179, 2097133, 15]-code), using construction X applied to Ce(13) ⊂ Ce(6) based on
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1286, 27, F128, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), 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(12846, 2097179, F128, 2, 14) (dual of [(2097179, 2), 4194312, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12846, 2097179, F128, 3, 14) (dual of [(2097179, 3), 6291491, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(12846, 2097179, F128, 4, 14) (dual of [(2097179, 4), 8388670, 15]-NRT-code) | [i] | ||
| 4 | Digital (32, 46, 2097179)-net over F128 | [i] | ||
| 5 | Linear OOA(12846, 1048589, F128, 2, 14) (dual of [(1048589, 2), 2097132, 15]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12846, 699059, F128, 3, 14) (dual of [(699059, 3), 2097131, 15]-NRT-code) | [i] | ||
| 7 | Linear OOA(12846, 524294, F128, 4, 14) (dual of [(524294, 4), 2097130, 15]-NRT-code) | [i] | ||
| 8 | Linear OOA(12846, 299597, F128, 14, 14) (dual of [(299597, 14), 4194312, 15]-NRT-code) | [i] | OA Folding and Stacking | |