Information on Result #1718986
Digital (100, 123, 2270)-net over F4, using net defined by OOA based on linear OOA(4123, 2270, F4, 27, 23) (dual of [(2270, 27), 61167, 24]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4123, 9081, F4, 3, 23) (dual of [(9081, 3), 27120, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4123, 9084, F4, 3, 23) (dual of [(9084, 3), 27129, 24]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4123, 9084, F4, 23) (dual of [9084, 8961, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4123, 16402, F4, 23) (dual of [16402, 16279, 24]-code), using
- construction XX applied to Ce(22) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(41, 16, F4, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(22) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4123, 16402, F4, 23) (dual of [16402, 16279, 24]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4123, 9084, F4, 23) (dual of [9084, 8961, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(4123, 9084, F4, 3, 23) (dual of [(9084, 3), 27129, 24]-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.