Information on Result #1723761
Linear OOA(5140, 19545, F5, 27, 23) (dual of [(19545, 27), 527575, 24]-NRT-code), using OOA 4-folding and stacking with additional row 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
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (117, 140, 19545)-net over F5 | [i] | Net Defined by OOA | |