Information on Result #1549253
Linear OOA(5112, 78181, F5, 3, 18) (dual of [(78181, 3), 234431, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5112, 78181, F5, 18) (dual of [78181, 78069, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5111, 78179, F5, 18) (dual of [78179, 78068, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(5111, 78180, F5, 17) (dual of [78180, 78069, 18]-code), using Gilbert–Varšamov bound and bm = 5111 > Vbs−1(k−1) = 399 151356 151647 618143 763208 153328 899826 104266 182399 537530 802971 890579 628285 [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(5111, 78179, F5, 18) (dual of [78179, 78068, 19]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(5112, 26060, F5, 21, 18) (dual of [(26060, 21), 547148, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |