Information on Result #731769

Linear OA(4137, 144, F4, 97) (dual of [144, 7, 98]-code), using juxtaposition based on
  1. linear OA(462, 69, F4, 46) (dual of [69, 7, 47]-code), using
    • construction X applied to C([1,140]) ⊂ C([1,128]) [i] based on
      1. linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using contraction [i] based on linear OA(4185, 189, F4, 140) (dual of [189, 4, 141]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,140], and designed minimum distance d ≥ |I|+1 = 141 [i]
      2. linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using contraction [i] based on linear OA(4182, 189, F4, 128) (dual of [189, 7, 129]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,128], and designed minimum distance d ≥ |I|+1 = 129 [i]
      3. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
  2. linear OA(468, 75, F4, 50) (dual of [75, 7, 51]-code), using
    • construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}), C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}) [i] based on
      1. linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}, and minimum distance d ≥ |{−4,−3,…,41}|+1 = 47 (BCH-bound) [i]
      2. linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}, and minimum distance d ≥ |{1,6,11,…,−26}|+1 = 47 (BCH-bound) [i]
      3. linear OA(462, 63, F4, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,4)), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}, and minimum distance d ≥ |{1,23,45,…,20}|+1 = 63 (BCH-bound) [i]
      4. linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 43 [i]
      5. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)) (see above)
      6. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)) (see above)

Mode: Constructive and 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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(4137, 144, F4, 96) (dual of [144, 7, 97]-code) [i]Strength Reduction
2Linear OOA(4137, 48, F4, 3, 97) (dual of [(48, 3), 7, 98]-NRT-code) [i]OOA Folding