Information on Result #899549
Linear OOA(2585, 4389641, F25, 2, 13) (dual of [(4389641, 2), 8779197, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2524, 195340, F25, 2, 6) (dual of [(195340, 2), 390656, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(253, 26, F25, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;49,25) [i]
- linear OOA(2521, 195314, F25, 2, 6) (dual of [(195314, 2), 390607, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2521, 390628, F25, 6) (dual of [390628, 390607, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2521, 390629, F25, 6) (dual of [390629, 390608, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2521, 390625, F25, 6) (dual of [390625, 390604, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2517, 390625, F25, 5) (dual of [390625, 390608, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2521, 390629, F25, 6) (dual of [390629, 390608, 7]-code), using
- OOA 2-folding [i] based on linear OA(2521, 390628, F25, 6) (dual of [390628, 390607, 7]-code), using
- linear OOA(253, 26, F25, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2561, 4194301, F25, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2561, 8388602, F25, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(2561, 8388602, F25, 13) (dual of [8388602, 8388541, 14]-code), using
Mode: Constructive and 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(2585, 1463213, F25, 14, 13) (dual of [(1463213, 14), 20484897, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |