Information on Result #1304113
Linear OA(337, 107, F3, 12) (dual of [107, 70, 13]-code), using 15 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 1, 0, 0, 0, 1, 5 times 0) based on linear OA(331, 86, F3, 12) (dual of [86, 55, 13]-code), using
- construction XX applied to C1 = C({0,1,2,4,5,7,8,53}), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,53}) [i] based on
- linear OA(329, 80, F3, 11) (dual of [80, 51, 12]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,53}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
- linear OA(327, 80, F3, 11) (dual of [80, 53, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(331, 80, F3, 12) (dual of [80, 49, 13]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,53}, and minimum distance d ≥ |{−1,0,…,10}|+1 = 13 (BCH-bound) [i]
- linear OA(325, 80, F3, 10) (dual of [80, 55, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(30, 2, F3, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
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.