Information on Result #1299880
Linear OA(465, 85, F4, 34) (dual of [85, 20, 35]-code), using construction X with Varšamov bound based on
- linear OA(464, 83, F4, 34) (dual of [83, 19, 35]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}), C2 = C([0,27]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}) [i] based on
- linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}, and minimum distance d ≥ |{−4,−3,…,25}|+1 = 31 (BCH-bound) [i]
- linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(456, 63, F4, 34) (dual of [63, 7, 35]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}, and minimum distance d ≥ |{−4,−3,…,29}|+1 = 35 (BCH-bound) [i]
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)), using
- linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)) (see above)
- construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}), C2 = C([0,27]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}) [i] based on
- linear OA(464, 84, F4, 33) (dual of [84, 20, 34]-code), using Gilbert–Varšamov bound and bm = 464 > Vbs−1(k−1) = 224 644425 322006 185581 484673 857770 119666 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.