Information on Result #1324238
Linear OA(4251, 4194390, F4, 29) (dual of [4194390, 4194139, 30]-code), using construction X with Varšamov bound based on
- linear OA(4247, 4194385, F4, 29) (dual of [4194385, 4194138, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4232, 4194304, F4, 29) (dual of [4194304, 4194072, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(415, 81, F4, 7) (dual of [81, 66, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4247, 4194386, F4, 25) (dual of [4194386, 4194139, 26]-code), using Gilbert–Varšamov bound and bm = 4247 > Vbs−1(k−1) = 400 143431 113171 697883 968484 820761 196144 224524 329654 586255 810060 373899 943514 826865 007467 314547 230568 188623 392751 897624 639769 028353 115804 283829 083576 [i]
- linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)), using
- dual of repetition code with length 4 [i]
- Reed–Solomon code RS(1,4) [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(4251, 2097195, F4, 2, 29) (dual of [(2097195, 2), 4194139, 30]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4251, 1398130, F4, 3, 29) (dual of [(1398130, 3), 4194139, 30]-NRT-code) | [i] | ||