Information on Result #1539407
Linear OOA(4174, 416759, F4, 3, 23) (dual of [(416759, 3), 1250103, 24]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4174, 416759, F4, 2, 23) (dual of [(416759, 2), 833344, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4174, 524299, F4, 2, 23) (dual of [(524299, 2), 1048424, 24]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4173, 524299, F4, 2, 23) (dual of [(524299, 2), 1048425, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4173, 1048598, F4, 23) (dual of [1048598, 1048425, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4172, 1048597, F4, 23) (dual of [1048597, 1048425, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4172, 1048597, F4, 23) (dual of [1048597, 1048425, 24]-code), using
- OOA 2-folding [i] based on linear OA(4173, 1048598, F4, 23) (dual of [1048598, 1048425, 24]-code), using
- 41 times duplication [i] based on linear OOA(4173, 524299, F4, 2, 23) (dual of [(524299, 2), 1048425, 24]-NRT-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, 104189, F4, 27, 23) (dual of [(104189, 27), 2812929, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |