Information on Result #1301864
Linear OA(5135, 390689, F5, 19) (dual of [390689, 390554, 20]-code), using construction X with Varšamov bound based on
- linear OA(5133, 390685, F5, 19) (dual of [390685, 390552, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- linear OA(5121, 390625, F5, 19) (dual of [390625, 390504, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(512, 60, F5, 6) (dual of [60, 48, 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(18) ⊂ Ce(11) [i] based on
- linear OA(5133, 390687, F5, 18) (dual of [390687, 390554, 19]-code), using Gilbert–Varšamov bound and bm = 5133 > Vbs−1(k−1) = 5 557485 131585 019656 100087 389072 219888 557414 736270 349062 156059 399125 095641 567493 712081 395625 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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.