Information on Result #1300737
Linear OA(4200, 16445, F4, 35) (dual of [16445, 16245, 36]-code), using construction X with Varšamov bound based on
- linear OA(4199, 16443, F4, 35) (dual of [16443, 16244, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(4183, 16385, F4, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(4199, 16444, F4, 34) (dual of [16444, 16245, 35]-code), using Gilbert–Varšamov bound and bm = 4199 > Vbs−1(k−1) = 8318 154608 206448 535144 098570 273705 403711 181624 503287 564574 289870 282181 037478 566598 645649 309222 798128 784842 461824 473606 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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
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.