Information on Result #686263
Linear OA(8100, 2097167, F8, 16) (dual of [2097167, 2097067, 17]-code), using construction X applied to Ce(16) ⊂ Ce(13) based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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 | Linear OOA(8100, 2097167, F8, 2, 16) (dual of [(2097167, 2), 4194234, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8100, 2097167, F8, 3, 16) (dual of [(2097167, 3), 6291401, 17]-NRT-code) | [i] | ||
| 3 | Digital (84, 100, 2097167)-net over F8 | [i] | ||
| 4 | Linear OOA(8100, 1048583, F8, 2, 16) (dual of [(1048583, 2), 2097066, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8100, 699055, F8, 3, 16) (dual of [(699055, 3), 2097065, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(8100, 262145, F8, 16, 16) (dual of [(262145, 16), 4194220, 17]-NRT-code) | [i] | OA Folding and Stacking | |