Information on Result #1423458
Linear OOA(4143, 52081, F4, 2, 22) (dual of [(52081, 2), 104019, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4143, 52081, F4, 22) (dual of [52081, 51938, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4143, 65590, F4, 22) (dual of [65590, 65447, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4142, 65589, F4, 22) (dual of [65589, 65447, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(413, 53, F4, 6) (dual of [53, 40, 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(21) ⊂ Ce(14) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4142, 65589, F4, 22) (dual of [65589, 65447, 23]-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(4143, 26040, F4, 3, 22) (dual of [(26040, 3), 77977, 23]-NRT-code) | [i] | OOA Folding | |