Information on Result #1323972
Linear OA(4170, 65603, F4, 26) (dual of [65603, 65433, 27]-code), using construction X with Varšamov bound based on
- linear OA(4167, 65598, F4, 26) (dual of [65598, 65431, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(414, 62, F4, 7) (dual of [62, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(4167, 65600, F4, 24) (dual of [65600, 65433, 25]-code), using Gilbert–Varšamov bound and bm = 4167 > Vbs−1(k−1) = 2230 006245 675231 862870 877376 588292 149471 727093 656059 154838 231967 223428 670660 051536 491771 855407 409960 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 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(4170, 32801, F4, 2, 26) (dual of [(32801, 2), 65432, 27]-NRT-code) | [i] | OOA Folding | |