Information on Result #1422777
Linear OOA(4131, 785033, F4, 2, 16) (dual of [(785033, 2), 1569935, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4131, 785033, F4, 16) (dual of [785033, 784902, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4131, 1048636, F4, 16) (dual of [1048636, 1048505, 17]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [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(4131, 392516, F4, 3, 16) (dual of [(392516, 3), 1177417, 17]-NRT-code) | [i] | OOA Folding | |