Information on Result #1365205
Linear OOA(4252, 2097196, F4, 2, 29) (dual of [(2097196, 2), 4194140, 30]-NRT-code), using OOA 2-folding based on linear OA(4252, 4194392, F4, 29) (dual of [4194392, 4194140, 30]-code), using
- construction X with Varšamov bound [i] 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, 4194387, F4, 25) (dual of [4194387, 4194140, 26]-code), using Gilbert–Varšamov bound and bm = 4247 > Vbs−1(k−1) = 400 145720 720407 198331 671405 793988 499562 497519 605049 261769 130149 629490 084429 501462 204521 992542 187264 174443 830670 517633 763192 496745 606645 641903 379304 [i]
- linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reed–Solomon code RSe(2,4) [i]
- Simplex code S(2,4) [i]
- linear OA(4247, 4194385, F4, 29) (dual of [4194385, 4194138, 30]-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(4252, 2097196, F4, 3, 29) (dual of [(2097196, 3), 6291336, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (223, 252, 2097196)-net over F4 | [i] | ||