Information on Result #824570
Linear OOA(4193, 131083, F4, 2, 28) (dual of [(131083, 2), 261973, 29]-NRT-code), using OOA 2-folding based on linear OA(4193, 262166, F4, 28) (dual of [262166, 261973, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, 262167, F4, 28) (dual of [262167, 261974, 29]-code), using
- construction XX applied to Ce(28) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 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
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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
- construction XX applied to Ce(28) ⊂ Ce(25) ⊂ Ce(24) [i] based on
Mode: Constructive and 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(4193, 131083, F4, 3, 28) (dual of [(131083, 3), 393056, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (165, 193, 131083)-net over F4 | [i] | ||