Information on Result #2496398
Linear OOA(4174, 131077, F4, 2, 26) (dual of [(131077, 2), 261980, 27]-NRT-code), using 41 times duplication based on linear OOA(4173, 131077, F4, 2, 26) (dual of [(131077, 2), 261981, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4173, 262154, F4, 26) (dual of [262154, 261981, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4172, 262153, F4, 26) (dual of [262153, 261981, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 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(40, 9, F4, 0) (dual of [9, 9, 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 X applied to Ce(25) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4172, 262153, F4, 26) (dual of [262153, 261981, 27]-code), using
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(4174, 99912, F4, 3, 26) (dual of [(99912, 3), 299562, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (148, 174, 99912)-net over F4 | [i] | ||