Information on Result #1307950
Linear OA(4127, 4286, F4, 26) (dual of [4286, 4159, 27]-code), using 172 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 26 times 0, 1, 40 times 0, 1, 62 times 0) based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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
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(4127, 4286, F4, 2, 26) (dual of [(4286, 2), 8445, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4127, 4286, F4, 3, 26) (dual of [(4286, 3), 12731, 27]-NRT-code) | [i] | ||
| 3 | Digital (101, 127, 4286)-net over F4 | [i] | ||
| 4 | Linear OOA(4127, 2143, F4, 2, 26) (dual of [(2143, 2), 4159, 27]-NRT-code) | [i] | OOA Folding | |