Information on Result #1723631
Linear OOA(5134, 19545, F5, 27, 22) (dual of [(19545, 27), 527581, 23]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(5134, 78181, F5, 3, 22) (dual of [(78181, 3), 234409, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5134, 78182, F5, 3, 22) (dual of [(78182, 3), 234412, 23]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5134, 78182, F5, 22) (dual of [78182, 78048, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5133, 78180, F5, 22) (dual of [78180, 78047, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(513, 55, F5, 7) (dual of [55, 42, 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(21) ⊂ Ce(13) [i] based on
- linear OA(5133, 78181, F5, 21) (dual of [78181, 78048, 22]-code), using Gilbert–Varšamov bound and bm = 5133 > Vbs−1(k−1) = 32 806565 410812 207250 510845 967978 929410 968263 921040 994583 886449 120376 063787 004305 770474 169585 [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(5133, 78180, F5, 22) (dual of [78180, 78047, 23]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5134, 78182, F5, 22) (dual of [78182, 78048, 23]-code), using
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 (112, 134, 19545)-net over F5 | [i] | Net Defined by OOA | |