Information on Result #1786085
Digital (59, 68, 1953157)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(568, 1953157, F5, 9) (dual of [1953157, 1953089, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(567, 1953155, F5, 9) (dual of [1953155, 1953088, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(567, 1953156, F5, 8) (dual of [1953156, 1953089, 9]-code), using Gilbert–Varšamov bound and bm = 567 > Vbs−1(k−1) = 352 486177 137451 133912 994108 051498 624472 670845 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(567, 1953155, F5, 9) (dual of [1953155, 1953088, 10]-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.