MinT - Information on Result #2241145

Information on Result #2241145

Linear OA(4¹⁶⁴, 209, F₄, 82) (dual of [209, 45, 83]-code), using 1 times truncation based on linear OA(4¹⁶⁵, 210, F₄, 83) (dual of [210, 45, 84]-code), using

concatenation of two codes [i] based on
1. linear OA(64²⁷, 42, F₆₄, 27) (dual of [42, 15, 28]-code or 42-arc in PG(26,64)), using
  - discarding factors / shortening the dual code based on linear OA(64²⁷, 64, F₆₄, 27) (dual of [64, 37, 28]-code or 64-arc in PG(26,64)), using
    - Reedâ€“Solomon code RS(37,64) [i]
2. linear OA(4², 5, F₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
  - extended Reedâ€“Solomon code RS_e(3,4) [i]
  - Hamming code H(2,4) [i]

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:

	Result		This result only	Method
1	Linear OOA(4¹⁶⁴, 104, F₄, 2, 82) (dual of [(104, 2), 44, 83]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4¹⁶⁴, 69, F₄, 3, 82) (dual of [(69, 3), 43, 83]-NRT-code)	[i]		OOA Folding