Information on Result #1785967
Digital (51, 63, 15659)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(563, 15659, F5, 12) (dual of [15659, 15596, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(561, 15655, F5, 12) (dual of [15655, 15594, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(531, 15625, F5, 7) (dual of [15625, 15594, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [i] based on
- linear OA(561, 15657, F5, 11) (dual of [15657, 15596, 12]-code), using Gilbert–Varšamov bound and bm = 561 > Vbs−1(k−1) = 254956 363865 960213 266248 448959 617731 264865 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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(561, 15655, F5, 12) (dual of [15655, 15594, 13]-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.