Information on Result #1323892
Linear OA(4107, 65587, F4, 16) (dual of [65587, 65480, 17]-code), using construction X with Varšamov bound based on
- linear OA(4106, 65585, F4, 16) (dual of [65585, 65479, 17]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(457, 65536, F4, 10) (dual of [65536, 65479, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(49, 49, F4, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(4106, 65586, F4, 15) (dual of [65586, 65480, 16]-code), using Gilbert–Varšamov bound and bm = 4106 > Vbs−1(k−1) = 1492 728460 061535 490508 264951 656682 458478 861342 597163 103179 070036 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(4107, 65587, F4, 2, 16) (dual of [(65587, 2), 131067, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4107, 65587, F4, 3, 16) (dual of [(65587, 3), 196654, 17]-NRT-code) | [i] | ||
| 3 | Digital (91, 107, 65587)-net over F4 | [i] | ||