Information on Result #1302522
Linear OA(868, 4109, F8, 19) (dual of [4109, 4041, 20]-code), using construction X with Varšamov bound based on
- linear OA(866, 4106, F8, 19) (dual of [4106, 4040, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(865, 4097, F8, 19) (dual of [4097, 4032, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(857, 4097, F8, 17) (dual of [4097, 4040, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(866, 4107, F8, 17) (dual of [4107, 4041, 18]-code), using Gilbert–Varšamov bound and bm = 866 > Vbs−1(k−1) = 10073 639137 123345 883541 440737 756827 700478 183014 272757 122304 [i]
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
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.