Information on Result #1420289
Linear OOA(457, 262166, F4, 2, 8) (dual of [(262166, 2), 524275, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(457, 262166, F4, 8) (dual of [262166, 262109, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(456, 262164, F4, 8) (dual of [262164, 262108, 9]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(437, 262144, F4, 6) (dual of [262144, 262107, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
- dual of repetition code with length 20 [i]
- linear OA(41, 20, F4, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(456, 262165, F4, 7) (dual of [262165, 262109, 8]-code), using Gilbert–Varšamov bound and bm = 456 > Vbs−1(k−1) = 328 709173 709519 950796 736532 717564 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(456, 262164, F4, 8) (dual of [262164, 262108, 9]-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(457, 131083, F4, 3, 8) (dual of [(131083, 3), 393192, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(457, 131082, F4, 10, 8) (dual of [(131082, 10), 1310763, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |