Information on Result #1021401
Linear OOA(5139, 5637065, F5, 3, 11) (dual of [(5637065, 3), 16911056, 12]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(52, 6, F5, 3, 2) (dual of [(6, 3), 16, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;16,5) [i]
- linear OOA(55, 781, F5, 3, 2) (dual of [(781, 3), 2338, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(55, 781, F5, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
- appending kth column [i] based on linear OA(55, 781, F5, 2) (dual of [781, 776, 3]-code), using
- Hamming code H(5,5) [i]
- appending kth column [i] based on linear OA(55, 781, F5, 2) (dual of [781, 776, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(55, 781, F5, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
- linear OOA(511, 43876, F5, 3, 3) (dual of [(43876, 3), 131617, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(511, 43876, F5, 2, 3) (dual of [(43876, 2), 87741, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(511, 43876, F5, 3) (dual of [43876, 43865, 4]-code or 43876-cap in PG(10,5)), using
- appending kth column [i] based on linear OOA(511, 43876, F5, 2, 3) (dual of [(43876, 2), 87741, 4]-NRT-code), using
- linear OOA(540, 2796201, F5, 3, 5) (dual of [(2796201, 3), 8388563, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(540, 4194301, F5, 3, 5) (dual of [(4194301, 3), 12582863, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(540, 4194301, F5, 3, 5) (dual of [(4194301, 3), 12582863, 6]-NRT-code), using
- linear OOA(581, 2796201, F5, 3, 11) (dual of [(2796201, 3), 8388522, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-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.