Information on Result #699800
Linear OA(12852, 2097179, F128, 16) (dual of [2097179, 2097127, 17]-code), using construction X applied to Ce(15) ⊂ Ce(8) based on
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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 | OA(3273, 2097179, S32, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12852, 2097179, F128, 2, 16) (dual of [(2097179, 2), 4194306, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12852, 2097179, F128, 3, 16) (dual of [(2097179, 3), 6291485, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(12852, 2097179, F128, 4, 16) (dual of [(2097179, 4), 8388664, 17]-NRT-code) | [i] | ||
| 5 | Digital (36, 52, 2097179)-net over F128 | [i] | ||
| 6 | Linear OOA(12852, 1048589, F128, 2, 16) (dual of [(1048589, 2), 2097126, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12852, 699059, F128, 3, 16) (dual of [(699059, 3), 2097125, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(12852, 524294, F128, 4, 16) (dual of [(524294, 4), 2097124, 17]-NRT-code) | [i] | ||
| 9 | Linear OOA(12852, 262147, F128, 16, 16) (dual of [(262147, 16), 4194300, 17]-NRT-code) | [i] | OA Folding and Stacking | |