Information on Result #1424600
Linear OOA(4160, 16433, F4, 2, 28) (dual of [(16433, 2), 32706, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4160, 16433, F4, 28) (dual of [16433, 16273, 29]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4157, 16428, F4, 28) (dual of [16428, 16271, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(49, 44, F4, 5) (dual of [44, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4157, 16430, F4, 26) (dual of [16430, 16273, 27]-code), using Gilbert–Varšamov bound and bm = 4157 > Vbs−1(k−1) = 131 810576 289040 175058 322088 251088 002285 240290 929852 635932 974484 216571 335842 766915 721909 205392 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 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(4157, 16428, F4, 28) (dual of [16428, 16271, 29]-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(4160, 8216, F4, 3, 28) (dual of [(8216, 3), 24488, 29]-NRT-code) | [i] | OOA Folding | |