Information on Result #1302158
Linear OA(771, 4808, F7, 18) (dual of [4808, 4737, 19]-code), using construction X with Varšamov bound based on
- linear OA(770, 4806, F7, 18) (dual of [4806, 4736, 19]-code), using
- trace code [i] based on linear OA(4935, 2403, F49, 18) (dual of [2403, 2368, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4935, 2401, F49, 18) (dual of [2401, 2366, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- trace code [i] based on linear OA(4935, 2403, F49, 18) (dual of [2403, 2368, 19]-code), using
- linear OA(770, 4807, F7, 17) (dual of [4807, 4737, 18]-code), using Gilbert–Varšamov bound and bm = 770 > Vbs−1(k−1) = 10659 258118 546356 219886 389296 729365 201105 633750 433978 744209 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.