Information on Result #1722116
Digital (48, 59, 19533)-net over F5, using net defined by OOA based on linear OOA(559, 19533, F5, 15, 11) (dual of [(19533, 15), 292936, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(559, 39067, F5, 3, 11) (dual of [(39067, 3), 117142, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(559, 39067, F5, 2, 11) (dual of [(39067, 2), 78075, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(559, 78134, F5, 11) (dual of [78134, 78075, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(559, 78135, F5, 11) (dual of [78135, 78076, 12]-code), using
- construction XX applied to Ce(10) ⊂ Ce(8) ⊂ Ce(7) [i] based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(10) ⊂ Ce(8) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(559, 78135, F5, 11) (dual of [78135, 78076, 12]-code), using
- OOA 2-folding [i] based on linear OA(559, 78134, F5, 11) (dual of [78134, 78075, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(559, 39067, F5, 2, 11) (dual of [(39067, 2), 78075, 12]-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.