Information on Result #1301929
Linear OA(5147, 78181, F5, 24) (dual of [78181, 78034, 25]-code), using construction X with Varšamov bound based on
- linear OA(5146, 78179, F5, 24) (dual of [78179, 78033, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(5146, 78180, F5, 23) (dual of [78180, 78034, 24]-code), using Gilbert–Varšamov bound and bm = 5146 > Vbs−1(k−1) = 6938 776015 260409 261300 233590 117089 269528 791590 690391 360796 093666 466329 963831 287365 834077 508651 671805 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 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.