Information on Result #1540904
Linear OOA(4195, 16453, F4, 3, 34) (dual of [(16453, 3), 49164, 35]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4195, 16453, F4, 34) (dual of [16453, 16258, 35]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4194, 16451, F4, 34) (dual of [16451, 16257, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(418, 67, F4, 8) (dual of [67, 49, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 68, F4, 8) (dual of [68, 50, 9]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- linear OA(4194, 16452, F4, 33) (dual of [16452, 16258, 34]-code), using Gilbert–Varšamov bound and bm = 4194 > Vbs−1(k−1) = 5 662938 997901 013253 120575 521818 338673 923901 746321 457859 516112 002258 730929 634579 370329 981557 669641 776631 370347 615270 [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(4194, 16451, F4, 34) (dual of [16451, 16257, 35]-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(4195, 2742, F4, 39, 34) (dual of [(2742, 39), 106743, 35]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |