Information on Result #1733790
Digital (15, 21, 32769)-net over F16, using net defined by OOA based on linear OOA(1621, 32769, F16, 10, 6) (dual of [(32769, 10), 327669, 7]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1621, 65539, F16, 2, 6) (dual of [(65539, 2), 131057, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1621, 65540, F16, 2, 6) (dual of [(65540, 2), 131059, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1621, 65540, F16, 6) (dual of [65540, 65519, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(1621, 65536, F16, 6) (dual of [65536, 65515, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1617, 65536, F16, 5) (dual of [65536, 65519, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1621, 65540, F16, 6) (dual of [65540, 65519, 7]-code), using
- discarding factors / shortening the dual code based on linear OOA(1621, 65540, F16, 2, 6) (dual of [(65540, 2), 131059, 7]-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.