Information on Result #1538426
Linear OOA(4159, 42958, F4, 3, 25) (dual of [(42958, 3), 128715, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4159, 42958, F4, 25) (dual of [42958, 42799, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4159, 65590, F4, 25) (dual of [65590, 65431, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4158, 65589, F4, 25) (dual of [65589, 65431, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(24) ⊂ Ce(17) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4158, 65589, F4, 25) (dual of [65589, 65431, 26]-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(4159, 10739, F4, 27, 25) (dual of [(10739, 27), 289794, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |