Information on Result #2799178
Linear OOA(3240, 398589, F3, 4, 27) (dual of [(398589, 4), 1594116, 28]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3236, 398588, F3, 4, 27) (dual of [(398588, 4), 1594116, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3236, 1594352, F3, 27) (dual of [1594352, 1594116, 28]-code), using
- construction X4 applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(3235, 1594324, F3, 27) (dual of [1594324, 1594089, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
- dual of repetition code with length 28 [i]
- linear OA(31, 28, F3, 1) (dual of [28, 27, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,13]) ⊂ C([0,12]) [i] based on
Mode: Constructive and 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(3240, 398589, F3, 5, 27) (dual of [(398589, 5), 1992705, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (213, 240, 398589)-net over F3 | [i] | ||