Information on Result #1725880
Digital (60, 78, 4405)-net over F7, using net defined by OOA based on linear OOA(778, 4405, F7, 21, 18) (dual of [(4405, 21), 92427, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(778, 13216, F7, 3, 18) (dual of [(13216, 3), 39570, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(778, 13216, F7, 18) (dual of [13216, 13138, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(778, 16820, F7, 18) (dual of [16820, 16742, 19]-code), using
- construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(14) [i] based on
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(71, 12, F7, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(17) ⊂ Ce(15) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(778, 16820, F7, 18) (dual of [16820, 16742, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(778, 13216, F7, 18) (dual of [13216, 13138, 19]-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.