Information on Result #899633
Linear OOA(2587, 4194641, F25, 2, 15) (dual of [(4194641, 2), 8389195, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2516, 340, F25, 2, 7) (dual of [(340, 2), 664, 8]-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(2513, 314, F25, 2, 7) (dual of [(314, 2), 615, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2513, 628, F25, 7) (dual of [628, 615, 8]-code), using
- construction XX applied to C1 = C([623,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([623,5]) [i] based on
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [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(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [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(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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([623,5]) [i] based on
- OOA 2-folding [i] based on linear OA(2513, 628, F25, 7) (dual of [628, 615, 8]-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(2571, 4194301, F25, 2, 15) (dual of [(4194301, 2), 8388531, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2571, 8388602, F25, 15) (dual of [8388602, 8388531, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- OOA 2-folding [i] based on linear OA(2571, 8388602, F25, 15) (dual of [8388602, 8388531, 16]-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.