Information on Result #1423577
Linear OOA(4145, 4288, F4, 2, 30) (dual of [(4288, 2), 8431, 31]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4145, 4288, F4, 30) (dual of [4288, 4143, 31]-code), using
- 174 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 10 times 0, 1, 16 times 0, 1, 26 times 0, 1, 41 times 0, 1, 62 times 0) [i] based on linear OA(4133, 4102, F4, 30) (dual of [4102, 3969, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
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(4145, 2144, F4, 3, 30) (dual of [(2144, 3), 6287, 31]-NRT-code) | [i] | OOA Folding | |