Information on Result #1306292
Linear OA(3136, 163, F3, 64) (dual of [163, 27, 65]-code), using 11 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1) based on linear OA(3113, 129, F3, 64) (dual of [129, 16, 65]-code), using
- construction XX applied to C1 = C([0,60]), C2 = C([1,66]), C3 = C1 + C2 = C([1,60]), and C∩ = C1 ∩ C2 = C([0,66]) [i] based on
- linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
- linear OA(3110, 121, F3, 66) (dual of [121, 11, 67]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,66], and designed minimum distance d ≥ |I|+1 = 67 [i]
- linear OA(3111, 121, F3, 68) (dual of [121, 10, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,66], and minimum distance d ≥ |{−1,0,…,66}|+1 = 69 (BCH-bound) [i]
- linear OA(3105, 121, F3, 60) (dual of [121, 16, 61]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,60], and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-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.