Information on Result #1545843
Linear OOA(4250, 65626, F4, 3, 38) (dual of [(65626, 3), 196628, 39]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4250, 65626, F4, 38) (dual of [65626, 65376, 39]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4249, 65624, F4, 38) (dual of [65624, 65375, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(26) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(424, 88, F4, 10) (dual of [88, 64, 11]-code), using
- construction X applied to Ce(37) ⊂ Ce(26) [i] based on
- linear OA(4249, 65625, F4, 37) (dual of [65625, 65376, 38]-code), using Gilbert–Varšamov bound and bm = 4249 > Vbs−1(k−1) = 103752 026953 041799 008742 905528 830794 308943 709294 972083 843181 513866 556558 403565 017500 407579 192529 844560 246539 149863 190072 913524 355080 732000 216583 669966 [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(4249, 65624, F4, 38) (dual of [65624, 65375, 39]-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(4250, 9375, F4, 45, 38) (dual of [(9375, 45), 421625, 39]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |