Information on Result #823221
Linear OOA(4110, 131082, F4, 2, 16) (dual of [(131082, 2), 262054, 17]-NRT-code), using OOA 2-folding based on linear OA(4110, 262164, F4, 16) (dual of [262164, 262054, 17]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(491, 262144, F4, 14) (dual of [262144, 262053, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
- dual of repetition code with length 20 [i]
- linear OA(41, 20, F4, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(4112, 131083, F4, 2, 16) (dual of [(131083, 2), 262054, 17]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4111, 131082, F4, 2, 16) (dual of [(131082, 2), 262053, 17]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4110, 131082, F4, 3, 16) (dual of [(131082, 3), 393136, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (94, 110, 131082)-net over F4 | [i] | ||