Information on Result #1543519
Linear OOA(4226, 15235, F4, 3, 41) (dual of [(15235, 3), 45479, 42]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4226, 15235, F4, 41) (dual of [15235, 15009, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(4226, 16434, F4, 41) (dual of [16434, 16208, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4224, 16432, F4, 41) (dual of [16432, 16208, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(33) [i] based on
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(413, 48, F4, 6) (dual of [48, 35, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(40) ⊂ Ce(33) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4224, 16432, F4, 41) (dual of [16432, 16208, 42]-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(4226, 2176, F4, 45, 41) (dual of [(2176, 45), 97694, 42]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |