Information on Result #899537
Linear OOA(2573, 4194616, F25, 2, 13) (dual of [(4194616, 2), 8389159, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2512, 315, F25, 2, 6) (dual of [(315, 2), 618, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2512, 630, F25, 6) (dual of [630, 618, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(2511, 625, F25, 6) (dual of [625, 614, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(257, 625, F25, 4) (dual of [625, 618, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(2512, 630, F25, 6) (dual of [630, 618, 7]-code), using
- 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(2573, 1398205, F25, 14, 13) (dual of [(1398205, 14), 19574797, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |