Information on Result #1494746
Linear OOA(6442, 3015, F64, 3, 17) (dual of [(3015, 3), 9003, 18]-NRT-code), using OOA 2-folding based on linear OOA(6442, 6030, F64, 2, 17) (dual of [(6030, 2), 12018, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6442, 6031, F64, 2, 17) (dual of [(6031, 2), 12020, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6442, 6031, F64, 17) (dual of [6031, 5989, 18]-code), using
- 1924 step Varšamov–Edel lengthening with (ri) = (4, 4 times 0, 1, 18 times 0, 1, 69 times 0, 1, 208 times 0, 1, 531 times 0, 1, 1088 times 0) [i] based on linear OA(6433, 4098, F64, 17) (dual of [4098, 4065, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(6433, 4096, F64, 17) (dual of [4096, 4063, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 1924 step Varšamov–Edel lengthening with (ri) = (4, 4 times 0, 1, 18 times 0, 1, 69 times 0, 1, 208 times 0, 1, 531 times 0, 1, 1088 times 0) [i] based on linear OA(6433, 4098, F64, 17) (dual of [4098, 4065, 18]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6442, 6031, F64, 17) (dual of [6031, 5989, 18]-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.