Information on Result #1609115
Linear OOA(3206, 187201, F3, 4, 24) (dual of [(187201, 4), 748598, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3206, 187201, F3, 2, 24) (dual of [(187201, 2), 374196, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3206, 265751, F3, 2, 24) (dual of [(265751, 2), 531296, 25]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3205, 265751, F3, 2, 24) (dual of [(265751, 2), 531297, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(3205, 265751, F3, 2, 25) (dual of [(265751, 2), 531297, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3205, 531502, F3, 25) (dual of [531502, 531297, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3204, 531501, F3, 25) (dual of [531501, 531297, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3193, 531442, F3, 25) (dual of [531442, 531249, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 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([0,12]) ⊂ C([0,9]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3204, 531501, F3, 25) (dual of [531501, 531297, 26]-code), using
- OOA 2-folding [i] based on linear OA(3205, 531502, F3, 25) (dual of [531502, 531297, 26]-code), using
- strength reduction [i] based on linear OOA(3205, 265751, F3, 2, 25) (dual of [(265751, 2), 531297, 26]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3205, 265751, F3, 2, 24) (dual of [(265751, 2), 531297, 25]-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(3206, 62400, F3, 28, 24) (dual of [(62400, 28), 1746994, 25]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |