Information on Result #1649844
Linear OOA(3220, 29262, F3, 5, 31) (dual of [(29262, 5), 146090, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3220, 29262, F3, 2, 31) (dual of [(29262, 2), 58304, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3220, 29559, F3, 2, 31) (dual of [(29559, 2), 58898, 32]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3218, 29558, F3, 2, 31) (dual of [(29558, 2), 58898, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3218, 59116, F3, 31) (dual of [59116, 58898, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(317, 67, F3, 7) (dual of [67, 50, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(3218, 59116, F3, 31) (dual of [59116, 58898, 32]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3218, 29558, F3, 2, 31) (dual of [(29558, 2), 58898, 32]-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(3220, 9753, F3, 35, 31) (dual of [(9753, 35), 341135, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |