Information on Result #1734776
Digital (59, 80, 10731)-net over F16, using net defined by OOA based on linear OOA(1680, 10731, F16, 22, 21) (dual of [(10731, 22), 236002, 22]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(1680, 53656, F16, 2, 21) (dual of [(53656, 2), 107232, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1680, 53660, F16, 2, 21) (dual of [(53660, 2), 107240, 22]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1680, 53660, F16, 21) (dual of [53660, 53580, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(1680, 65554, F16, 21) (dual of [65554, 65474, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(1677, 65536, F16, 21) (dual of [65536, 65459, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(1680, 65554, F16, 21) (dual of [65554, 65474, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1680, 53660, F16, 21) (dual of [53660, 53580, 22]-code), using
- discarding factors / shortening the dual code based on linear OOA(1680, 53660, F16, 2, 21) (dual of [(53660, 2), 107240, 22]-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.