Information on Result #1485814
Linear OOA(5121, 1863, F5, 3, 28) (dual of [(1863, 3), 5468, 29]-NRT-code), using OOA 2-folding based on linear OOA(5121, 3726, F5, 2, 28) (dual of [(3726, 2), 7331, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5121, 3726, F5, 28) (dual of [3726, 3605, 29]-code), using
- 586 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 31 times 0, 1, 63 times 0, 1, 109 times 0, 1, 158 times 0, 1, 195 times 0) [i] based on linear OA(5111, 3130, F5, 28) (dual of [3130, 3019, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(5111, 3125, F5, 28) (dual of [3125, 3014, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(5106, 3125, F5, 27) (dual of [3125, 3019, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 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
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- 586 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 31 times 0, 1, 63 times 0, 1, 109 times 0, 1, 158 times 0, 1, 195 times 0) [i] based on linear OA(5111, 3130, F5, 28) (dual of [3130, 3019, 29]-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.