Information on Result #1718520
Digital (132, 151, 174772)-net over F4, using net defined by OOA based on linear OOA(4151, 174772, F4, 21, 19) (dual of [(174772, 21), 3670061, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4151, 524317, F4, 3, 19) (dual of [(524317, 3), 1572800, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4151, 524318, F4, 3, 19) (dual of [(524318, 3), 1572803, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4151, 524318, F4, 2, 19) (dual of [(524318, 2), 1048485, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4151, 1048636, F4, 19) (dual of [1048636, 1048485, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(4141, 1048576, F4, 19) (dual of [1048576, 1048435, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- OOA 2-folding [i] based on linear OA(4151, 1048636, F4, 19) (dual of [1048636, 1048485, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4151, 524318, F4, 2, 19) (dual of [(524318, 2), 1048485, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4151, 524318, F4, 3, 19) (dual of [(524318, 3), 1572803, 20]-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.