Information on Result #1430007
Linear OOA(4213, 65613, F4, 2, 32) (dual of [(65613, 2), 131013, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4213, 65613, F4, 32) (dual of [65613, 65400, 33]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4212, 65611, F4, 32) (dual of [65611, 65399, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(419, 75, F4, 8) (dual of [75, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(419, 87, F4, 8) (dual of [87, 68, 9]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- linear OA(4212, 65612, F4, 31) (dual of [65612, 65400, 32]-code), using Gilbert–Varšamov bound and bm = 4212 > Vbs−1(k−1) = 2 491516 148176 583161 754533 376930 039343 273609 642617 689090 942386 863355 587601 404985 914567 139226 649891 556421 913112 673997 243819 444944 [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
- linear OA(4212, 65611, F4, 32) (dual of [65611, 65399, 33]-code), 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(4213, 32806, F4, 3, 32) (dual of [(32806, 3), 98205, 33]-NRT-code) | [i] | OOA Folding | |