Information on Result #1533111
Linear OOA(3245, 4194411, F3, 3, 22) (dual of [(4194411, 3), 12582988, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3245, 4194411, F3, 2, 22) (dual of [(4194411, 2), 8388577, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(334, 110, F3, 2, 11) (dual of [(110, 2), 186, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(334, 110, F3, 11) (dual of [110, 76, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(334, 115, F3, 11) (dual of [115, 81, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(333, 113, F3, 11) (dual of [113, 80, 12]-code), using
- a “BZ†code from Brouwer’s database [i]
- linear OA(333, 114, F3, 10) (dual of [114, 81, 11]-code), using Gilbert–Varšamov bound and bm = 333 > Vbs−1(k−1) = 3192 777628 940355 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(333, 113, F3, 11) (dual of [113, 80, 12]-code), using
- construction X with Varšamov bound [i] based on
- discarding factors / shortening the dual code based on linear OA(334, 115, F3, 11) (dual of [115, 81, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(334, 110, F3, 11) (dual of [110, 76, 12]-code), using
- linear OOA(3211, 4194301, F3, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- linear OOA(334, 110, F3, 2, 11) (dual of [(110, 2), 186, 12]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3245, 2097205, F3, 5, 22) (dual of [(2097205, 5), 10485780, 23]-NRT-code) | [i] | OOA Folding | |