Information on Result #1300331
Linear OA(4155, 4194360, F4, 18) (dual of [4194360, 4194205, 19]-code), using construction X with Varšamov bound based on
- linear OA(4152, 4194356, F4, 18) (dual of [4194356, 4194204, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 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(4152, 4194357, F4, 15) (dual of [4194357, 4194205, 16]-code), using Gilbert–Varšamov bound and bm = 4152 > Vbs−1(k−1) = 28615 037461 347694 872529 724392 167737 516198 309592 279422 407274 680482 820222 485907 318277 084596 [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]
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(4155, 2097180, F4, 2, 18) (dual of [(2097180, 2), 4194205, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4155, 1398120, F4, 3, 18) (dual of [(1398120, 3), 4194205, 19]-NRT-code) | [i] | ||