Information on Result #1323912
Linear OA(4133, 16435, F4, 23) (dual of [16435, 16302, 24]-code), using construction X with Varšamov bound based on
- linear OA(4129, 16428, F4, 23) (dual of [16428, 16299, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(49, 44, F4, 5) (dual of [44, 35, 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(22) ⊂ Ce(16) [i] based on
- linear OA(4129, 16431, F4, 21) (dual of [16431, 16302, 22]-code), using Gilbert–Varšamov bound and bm = 4129 > Vbs−1(k−1) = 2912 084288 117974 597007 097416 850026 879962 820932 812468 445015 688185 357118 952334 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 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: 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(4133, 16435, F4, 2, 23) (dual of [(16435, 2), 32737, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4133, 16435, F4, 3, 23) (dual of [(16435, 3), 49172, 24]-NRT-code) | [i] | ||
| 3 | Digital (110, 133, 16435)-net over F4 | [i] | ||