Information on Result #899785
Linear OOA(25105, 4194618, F25, 2, 18) (dual of [(4194618, 2), 8389131, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2519, 317, F25, 2, 9) (dual of [(317, 2), 615, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2519, 634, F25, 9) (dual of [634, 615, 10]-code), using
- construction XX applied to C1 = C([621,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([621,5]) [i] based on
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,4}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,5}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 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 XX applied to C1 = C([621,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([621,5]) [i] based on
- OOA 2-folding [i] based on linear OA(2519, 634, F25, 9) (dual of [634, 615, 10]-code), using
- linear OOA(2586, 4194301, F25, 2, 18) (dual of [(4194301, 2), 8388516, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2586, 8388602, F25, 18) (dual of [8388602, 8388516, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- OOA 2-folding [i] based on linear OA(2586, 8388602, F25, 18) (dual of [8388602, 8388516, 19]-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
None.