Information on Result #699778
Linear OA(12850, 2097171, F128, 16) (dual of [2097171, 2097121, 17]-code), using construction X applied to Ce(15) ⊂ Ce(10) 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(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), 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(1688, 2097171, S16, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3270, 2097171, S32, 16) | [i] | ||
| 3 | OA(6459, 2097171, S64, 16) | [i] | ||
| 4 | Linear OOA(12850, 1129501, F128, 2, 16) (dual of [(1129501, 2), 2258952, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12850, 1129501, F128, 3, 16) (dual of [(1129501, 3), 3388453, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(12850, 1129501, F128, 4, 16) (dual of [(1129501, 4), 4517954, 17]-NRT-code) | [i] | ||
| 7 | Digital (34, 50, 1129501)-net over F128 | [i] | ||
| 8 | Linear OOA(12850, 1048585, F128, 2, 16) (dual of [(1048585, 2), 2097120, 17]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12850, 699057, F128, 3, 16) (dual of [(699057, 3), 2097121, 17]-NRT-code) | [i] | ||
| 10 | Linear OOA(12850, 524292, F128, 4, 16) (dual of [(524292, 4), 2097118, 17]-NRT-code) | [i] | ||
| 11 | Linear OOA(12850, 262146, F128, 16, 16) (dual of [(262146, 16), 4194286, 17]-NRT-code) | [i] | OA Folding and Stacking | |