Information on Result #1736470
Digital (23, 39, 290)-net over F25, using net defined by OOA based on linear OOA(2539, 290, F25, 18, 16) (dual of [(290, 18), 5181, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(2539, 1161, F25, 2, 16) (dual of [(1161, 2), 2283, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2539, 1162, F25, 2, 16) (dual of [(1162, 2), 2285, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2539, 1162, F25, 16) (dual of [1162, 1123, 17]-code), using
- 526 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 39 times 0, 1, 91 times 0, 1, 157 times 0, 1, 217 times 0) [i] based on linear OA(2531, 628, F25, 16) (dual of [628, 597, 17]-code), using
- construction XX applied to C1 = C([623,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([623,14]) [i] based on
- linear OA(2529, 624, F25, 15) (dual of [624, 595, 16]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2529, 624, F25, 15) (dual of [624, 595, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2531, 624, F25, 16) (dual of [624, 593, 17]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2527, 624, F25, 14) (dual of [624, 597, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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([623,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([623,14]) [i] based on
- 526 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 39 times 0, 1, 91 times 0, 1, 157 times 0, 1, 217 times 0) [i] based on linear OA(2531, 628, F25, 16) (dual of [628, 597, 17]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2539, 1162, F25, 16) (dual of [1162, 1123, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(2539, 1162, F25, 2, 16) (dual of [(1162, 2), 2285, 17]-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.