Information on Result #1539408
Linear OOA(4174, 524319, F4, 3, 22) (dual of [(524319, 3), 1572783, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4174, 524319, F4, 2, 22) (dual of [(524319, 2), 1048464, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4174, 1048638, F4, 22) (dual of [1048638, 1048464, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, 1048639, F4, 22) (dual of [1048639, 1048465, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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]
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4174, 1048639, F4, 22) (dual of [1048639, 1048465, 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(4174, 131079, F4, 27, 22) (dual of [(131079, 27), 3538959, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |