Information on Result #1546157
Linear OOA(4253, 437400, F4, 3, 33) (dual of [(437400, 3), 1311947, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4253, 437400, F4, 2, 33) (dual of [(437400, 2), 874547, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4253, 524314, F4, 2, 33) (dual of [(524314, 2), 1048375, 34]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4252, 524314, F4, 2, 33) (dual of [(524314, 2), 1048376, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4252, 1048628, F4, 33) (dual of [1048628, 1048376, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4251, 1048627, F4, 33) (dual of [1048627, 1048376, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4201, 1048577, F4, 27) (dual of [1048577, 1048376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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([0,16]) ⊂ C([0,13]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4251, 1048627, F4, 33) (dual of [1048627, 1048376, 34]-code), using
- OOA 2-folding [i] based on linear OA(4252, 1048628, F4, 33) (dual of [1048628, 1048376, 34]-code), using
- 41 times duplication [i] based on linear OOA(4252, 524314, F4, 2, 33) (dual of [(524314, 2), 1048376, 34]-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(4253, 72899, F4, 39, 33) (dual of [(72899, 39), 2842808, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |