MinT - Information on Result #2202673

Information on Result #2202673

Linear OA(4¹⁵⁰, 210, F₄, 67) (dual of [210, 60, 68]-code), using strength reduction based on linear OA(4¹⁵⁰, 210, F₄, 68) (dual of [210, 60, 69]-code), using

concatenation of two codes [i] based on
1. linear OA(64²², 42, F₆₄, 22) (dual of [42, 20, 23]-code or 42-arc in PG(21,64)), using
  - discarding factors / shortening the dual code based on linear OA(64²², 64, F₆₄, 22) (dual of [64, 42, 23]-code or 64-arc in PG(21,64)), using
    - Reedâ€“Solomon code RS(42,64) [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		Method
1	Linear OA(4¹⁴⁹, 209, F₄, 66) (dual of [209, 60, 67]-code)	[i]	Truncation
2	Linear OOA(4¹⁵⁰, 105, F₄, 2, 67) (dual of [(105, 2), 60, 68]-NRT-code)	[i]	OOA Folding
3	Linear OOA(4¹⁵⁰, 70, F₄, 3, 67) (dual of [(70, 3), 60, 68]-NRT-code)	[i]	OOA Folding