Information on Result #1788861
Digital (119, 139, 390676)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5139, 390676, F5, 20) (dual of [390676, 390537, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5138, 390674, F5, 20) (dual of [390674, 390536, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(5138, 390675, F5, 19) (dual of [390675, 390537, 20]-code), using Gilbert–Varšamov bound and bm = 5138 > Vbs−1(k−1) = 482208 549110 957318 026650 961597 097225 589066 727263 344489 448345 145213 156603 669417 947892 021092 274649 [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
- linear OA(5138, 390674, F5, 20) (dual of [390674, 390536, 21]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.