Information on Result #1300901
Linear OA(4221, 16444, F4, 39) (dual of [16444, 16223, 40]-code), using construction X with Varšamov bound based on
- linear OA(4220, 16442, F4, 39) (dual of [16442, 16222, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(30) [i] based on
- linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- construction X applied to Ce(38) ⊂ Ce(30) [i] based on
- linear OA(4220, 16443, F4, 38) (dual of [16443, 16223, 39]-code), using Gilbert–Varšamov bound and bm = 4220 > Vbs−1(k−1) = 30746 338315 950008 498051 172737 233099 627332 152884 103927 485844 605905 521105 978689 695357 810390 880434 054220 935746 809902 569046 289446 090466 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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.