Information on Result #1721784
Digital (41, 48, 1953137)-net over F5, using net defined by OOA based on linear OOA(548, 1953137, F5, 9, 7) (dual of [(1953137, 9), 17578185, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(548, 1953138, F5, 3, 7) (dual of [(1953138, 3), 5859366, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(548, 1953138, F5, 7) (dual of [1953138, 1953090, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(547, 1953136, F5, 7) (dual of [1953136, 1953089, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(546, 1953125, F5, 7) (dual of [1953125, 1953079, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(510, 11, F5, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,5)), using
- dual of repetition code with length 11 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(547, 1953137, F5, 6) (dual of [1953137, 1953090, 7]-code), using Gilbert–Varšamov bound and bm = 547 > Vbs−1(k−1) = 242 537663 682937 878164 259189 631553 [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(547, 1953136, F5, 7) (dual of [1953136, 1953089, 8]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(548, 1953138, F5, 7) (dual of [1953138, 1953090, 8]-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.