Information on Result #1564864
Linear OOA(6473, 4867, F64, 3, 31) (dual of [(4867, 3), 14528, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(6473, 4867, F64, 31) (dual of [4867, 4794, 32]-code), using
- 754 step Varšamov–Edel lengthening with (ri) = (5, 0, 0, 1, 6 times 0, 1, 17 times 0, 1, 40 times 0, 1, 93 times 0, 1, 200 times 0, 1, 389 times 0) [i] based on linear OA(6462, 4102, F64, 31) (dual of [4102, 4040, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
- linear OA(6461, 4097, F64, 31) (dual of [4097, 4036, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(6457, 4097, F64, 29) (dual of [4097, 4040, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,15]) ⊂ C([0,14]) [i] based on
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(6473, 973, F64, 33, 31) (dual of [(973, 33), 32036, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |