Information on Result #2973313
Linear OOA(2113, 65541, F2, 7, 12) (dual of [(65541, 7), 458674, 13]-NRT-code), using 23 times duplication based on linear OOA(2110, 65541, F2, 7, 12) (dual of [(65541, 7), 458677, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2110, 65541, F2, 4, 12) (dual of [(65541, 4), 262054, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2110, 262164, F2, 12) (dual of [262164, 262054, 13]-code), using
- strength reduction [i] based on linear OA(2110, 262164, F2, 13) (dual of [262164, 262054, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2109, 262144, F2, 13) (dual of [262144, 262035, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- strength reduction [i] based on linear OA(2110, 262164, F2, 13) (dual of [262164, 262054, 14]-code), using
- OOA 4-folding [i] based on linear OA(2110, 262164, F2, 12) (dual of [262164, 262054, 13]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.