Information on Result #1479070
Linear OOA(4111, 8216, F4, 3, 19) (dual of [(8216, 3), 24537, 20]-NRT-code), using OOA 2-folding based on linear OOA(4111, 16432, F4, 2, 19) (dual of [(16432, 2), 32753, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4111, 16433, F4, 2, 19) (dual of [(16433, 2), 32755, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4111, 16433, F4, 19) (dual of [16433, 16322, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4109, 16429, F4, 19) (dual of [16429, 16320, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(4109, 16431, F4, 18) (dual of [16431, 16322, 19]-code), using Gilbert–Varšamov bound and bm = 4109 > Vbs−1(k−1) = 166872 685441 752513 722190 940821 059033 293816 304441 635352 717448 085054 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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
- linear OA(4109, 16429, F4, 19) (dual of [16429, 16320, 20]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4111, 16433, F4, 19) (dual of [16433, 16322, 20]-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.