Information on Result #1737596
Digital (59, 87, 2236)-net over F25, using net defined by OOA based on linear OOA(2587, 2236, F25, 30, 28) (dual of [(2236, 30), 66993, 29]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OOA(2587, 15653, F25, 2, 28) (dual of [(15653, 2), 31219, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2587, 15654, F25, 2, 28) (dual of [(15654, 2), 31221, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2587, 15654, F25, 28) (dual of [15654, 15567, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(258, 29, F25, 7) (dual of [29, 21, 8]-code), using
- construction X applied to AG(F,9P) ⊂ AG(F,10P) [i] based on
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,9P) ⊂ AG(F,10P) [i] based on
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2587, 15654, F25, 28) (dual of [15654, 15567, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(2587, 15654, F25, 2, 28) (dual of [(15654, 2), 31221, 29]-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.