Information on Result #1736192
Digital (16, 28, 258)-net over F25, using net defined by OOA based on linear OOA(2528, 258, F25, 14, 12) (dual of [(258, 14), 3584, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2528, 775, F25, 2, 12) (dual of [(775, 2), 1522, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2528, 776, F25, 2, 12) (dual of [(776, 2), 1524, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2528, 776, F25, 12) (dual of [776, 748, 13]-code), using
- 141 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 28 times 0, 1, 105 times 0) [i] based on linear OA(2524, 631, F25, 12) (dual of [631, 607, 13]-code), using
- construction XX applied to C1 = C([622,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([622,9]) [i] based on
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,9}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), 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([622,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([622,9]) [i] based on
- 141 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 28 times 0, 1, 105 times 0) [i] based on linear OA(2524, 631, F25, 12) (dual of [631, 607, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2528, 776, F25, 12) (dual of [776, 748, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(2528, 776, F25, 2, 12) (dual of [(776, 2), 1524, 13]-NRT-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.