Information on Result #1718426
Digital (78, 97, 1553)-net over F4, using net defined by OOA based on linear OOA(497, 1553, F4, 21, 19) (dual of [(1553, 21), 32516, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(497, 4660, F4, 3, 19) (dual of [(4660, 3), 13883, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(497, 4660, F4, 19) (dual of [4660, 4563, 20]-code), using
- 546 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 20 times 0, 1, 34 times 0, 1, 57 times 0, 1, 88 times 0, 1, 132 times 0, 1, 187 times 0) [i] based on linear OA(485, 4102, F4, 19) (dual of [4102, 4017, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(479, 4096, F4, 18) (dual of [4096, 4017, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- 546 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 20 times 0, 1, 34 times 0, 1, 57 times 0, 1, 88 times 0, 1, 132 times 0, 1, 187 times 0) [i] based on linear OA(485, 4102, F4, 19) (dual of [4102, 4017, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(497, 4660, F4, 19) (dual of [4660, 4563, 20]-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.