Information on Result #1537400
Linear OOA(4142, 524314, F4, 3, 18) (dual of [(524314, 3), 1572800, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4142, 524314, F4, 2, 18) (dual of [(524314, 2), 1048486, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4142, 1048628, F4, 18) (dual of [1048628, 1048486, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4139, 1048624, F4, 18) (dual of [1048624, 1048485, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4139, 1048625, F4, 15) (dual of [1048625, 1048486, 16]-code), using Gilbert–Varšamov bound and bm = 4139 > Vbs−1(k−1) = 106 642560 461792 409923 627689 380487 584874 430228 575430 777377 059074 615722 713981 444427 [i]
- linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [i]
- linear OA(4139, 1048624, F4, 18) (dual of [1048624, 1048485, 19]-code), using
- construction X with Varšamov bound [i] based on
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(4142, 174771, F4, 21, 18) (dual of [(174771, 21), 3670049, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |