Information on Result #1723762
Digital (117, 140, 19545)-net over F5, using net defined by OOA based on linear OOA(5140, 19545, F5, 27, 23) (dual of [(19545, 27), 527575, 24]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(5140, 78181, F5, 3, 23) (dual of [(78181, 3), 234403, 24]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5140, 78181, F5, 23) (dual of [78181, 78041, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5139, 78179, F5, 23) (dual of [78179, 78040, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [i] based on
- linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [i] based on
- linear OA(5139, 78180, F5, 22) (dual of [78180, 78041, 23]-code), using Gilbert–Varšamov bound and bm = 5139 > Vbs−1(k−1) = 488282 018122 615488 776625 588723 256827 563722 393840 563813 717573 349059 141483 832043 660451 166042 939645 [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(5139, 78179, F5, 23) (dual of [78179, 78040, 24]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5140, 78181, F5, 23) (dual of [78181, 78041, 24]-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.