Information on Result #1540683
Linear OOA(4192, 477887, F4, 3, 25) (dual of [(477887, 3), 1433469, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4192, 477887, F4, 2, 25) (dual of [(477887, 2), 955582, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4192, 524314, F4, 2, 25) (dual of [(524314, 2), 1048436, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4192, 1048628, F4, 25) (dual of [1048628, 1048436, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4191, 1048627, F4, 25) (dual of [1048627, 1048436, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4141, 1048577, F4, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(410, 50, F4, 5) (dual of [50, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 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(4191, 1048627, F4, 25) (dual of [1048627, 1048436, 26]-code), using
- OOA 2-folding [i] based on linear OA(4192, 1048628, F4, 25) (dual of [1048628, 1048436, 26]-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(4192, 119471, F4, 27, 25) (dual of [(119471, 27), 3225525, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |