Information on Result #1717424
Digital (27, 37, 318)-net over F4, using net defined by OOA based on linear OOA(437, 318, F4, 15, 10) (dual of [(318, 15), 4733, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(437, 637, F4, 3, 10) (dual of [(637, 3), 1874, 11]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(437, 637, F4, 10) (dual of [637, 600, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(437, 1034, F4, 10) (dual of [1034, 997, 11]-code), using
- construction XX applied to C1 = C([333,341]), C2 = C([335,342]), C3 = C1 + C2 = C([335,341]), and C∩ = C1 ∩ C2 = C([333,342]) [i] based on
- linear OA(431, 1023, F4, 9) (dual of [1023, 992, 10]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {333,334,…,341}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(431, 1023, F4, 8) (dual of [1023, 992, 9]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {335,336,…,342}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(436, 1023, F4, 10) (dual of [1023, 987, 11]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {333,334,…,342}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {335,336,…,341}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([333,341]), C2 = C([335,342]), C3 = C1 + C2 = C([335,341]), and C∩ = C1 ∩ C2 = C([333,342]) [i] based on
- discarding factors / shortening the dual code based on linear OA(437, 1034, F4, 10) (dual of [1034, 997, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(437, 637, F4, 10) (dual of [637, 600, 11]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.