Information on Result #1300741
Linear OA(4204, 4194378, F4, 23) (dual of [4194378, 4194174, 24]-code), using construction X with Varšamov bound based on
- linear OA(4199, 4194370, F4, 23) (dual of [4194370, 4194171, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(411, 66, F4, 5) (dual of [66, 55, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(411, 68, F4, 5) (dual of [68, 57, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(47, 64, F4, 3) (dual of [64, 57, 4]-code or 64-cap in PG(6,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(411, 68, F4, 5) (dual of [68, 57, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4199, 4194373, F4, 20) (dual of [4194373, 4194174, 21]-code), using Gilbert–Varšamov bound and bm = 4199 > Vbs−1(k−1) = 6469 401928 124758 600511 055968 905137 835850 168973 772002 241560 402035 015076 555586 997530 403579 033003 937475 227984 367394 487940 [i]
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
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.