Information on Result #1480164
Linear OOA(4173, 2084, F4, 3, 37) (dual of [(2084, 3), 6079, 38]-NRT-code), using OOA 2-folding based on linear OOA(4173, 4168, F4, 2, 37) (dual of [(4168, 2), 8163, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4173, 4169, F4, 2, 37) (dual of [(4169, 2), 8165, 38]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4173, 4169, F4, 37) (dual of [4169, 3996, 38]-code), using
- 57 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 8 times 0, 1, 13 times 0, 1, 22 times 0) [i] based on linear OA(4164, 4103, F4, 37) (dual of [4103, 3939, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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(36) ⊂ Ce(34) [i] based on
- 57 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 8 times 0, 1, 13 times 0, 1, 22 times 0) [i] based on linear OA(4164, 4103, F4, 37) (dual of [4103, 3939, 38]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4173, 4169, F4, 37) (dual of [4169, 3996, 38]-code), 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.