Information on Result #1364925
Linear OOA(4173, 524315, F4, 2, 22) (dual of [(524315, 2), 1048457, 23]-NRT-code), using OOA 2-folding based on linear OA(4173, 1048630, F4, 22) (dual of [1048630, 1048457, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4169, 1048624, F4, 22) (dual of [1048624, 1048455, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- linear OA(4169, 1048626, F4, 19) (dual of [1048626, 1048457, 20]-code), using Gilbert–Varšamov bound and bm = 4169 > Vbs−1(k−1) = 142214 676168 425687 962382 179001 005364 558602 026249 348256 279316 539898 592853 537950 928498 269324 977246 760376 [i]
- linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reed–Solomon code RS(2,4) [i]
- linear OA(4169, 1048624, F4, 22) (dual of [1048624, 1048455, 23]-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(4173, 524315, F4, 3, 22) (dual of [(524315, 3), 1572772, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (151, 173, 524315)-net over F4 | [i] | ||