Information on Result #1723890
Digital (124, 148, 19547)-net over F5, using net defined by OOA based on linear OOA(5148, 19547, F5, 27, 24) (dual of [(19547, 27), 527621, 25]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(5148, 78189, F5, 3, 24) (dual of [(78189, 3), 234419, 25]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5148, 78189, F5, 24) (dual of [78189, 78041, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5147, 78187, F5, 24) (dual of [78187, 78040, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(513, 62, F5, 7) (dual of [62, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- linear OA(5147, 78188, F5, 23) (dual of [78188, 78041, 24]-code), using Gilbert–Varšamov bound and bm = 5147 > Vbs−1(k−1) = 6954 415740 943782 753630 051600 992062 632249 132417 623138 635593 651920 378621 944793 628392 308548 326966 386525 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5147, 78187, F5, 24) (dual of [78187, 78040, 25]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5148, 78189, F5, 24) (dual of [78189, 78041, 25]-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.