Information on Result #1650931
Linear OOA(3232, 63323, F3, 5, 30) (dual of [(63323, 5), 316383, 31]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3232, 63323, F3, 2, 30) (dual of [(63323, 2), 126414, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3232, 88601, F3, 2, 30) (dual of [(88601, 2), 176970, 31]-NRT-code), using
- strength reduction [i] based on linear OOA(3232, 88601, F3, 2, 31) (dual of [(88601, 2), 176970, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3232, 177202, F3, 31) (dual of [177202, 176970, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3232, 177203, F3, 31) (dual of [177203, 176971, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3221, 177148, F3, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3177, 177148, F3, 25) (dual of [177148, 176971, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3232, 177203, F3, 31) (dual of [177203, 176971, 32]-code), using
- OOA 2-folding [i] based on linear OA(3232, 177202, F3, 31) (dual of [177202, 176970, 32]-code), using
- strength reduction [i] based on linear OOA(3232, 88601, F3, 2, 31) (dual of [(88601, 2), 176970, 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(3232, 21107, F3, 35, 30) (dual of [(21107, 35), 738513, 31]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |