Information on Result #1426832
Linear OOA(4184, 4265, F4, 2, 39) (dual of [(4265, 2), 8346, 40]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4184, 4265, F4, 39) (dual of [4265, 4081, 40]-code), using
- 154 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 40 times 0, 1, 65 times 0) [i] based on linear OA(4175, 4102, F4, 39) (dual of [4102, 3927, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(38) ⊂ Ce(37) [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(4184, 2132, F4, 3, 39) (dual of [(2132, 3), 6212, 40]-NRT-code) | [i] | OOA Folding | |