Information on Result #1612019
Linear OOA(3238, 1594346, F3, 4, 24) (dual of [(1594346, 4), 6377146, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3238, 1594346, F3, 3, 24) (dual of [(1594346, 3), 4782800, 25]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3237, 1594346, F3, 3, 24) (dual of [(1594346, 3), 4782801, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(3237, 1594346, F3, 3, 25) (dual of [(1594346, 3), 4782801, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3237, 4783038, F3, 25) (dual of [4783038, 4782801, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 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(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-code), using
- OOA 3-folding [i] based on linear OA(3237, 4783038, F3, 25) (dual of [4783038, 4782801, 26]-code), using
- strength reduction [i] based on linear OOA(3237, 1594346, F3, 3, 25) (dual of [(1594346, 3), 4782801, 26]-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(3238, 531448, F3, 28, 24) (dual of [(531448, 28), 14880306, 25]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |