MinT - Information on Result #2202905

Information on Result #2202905

Linear OA(4¹⁵⁶, 210, F₄, 73) (dual of [210, 54, 74]-code), using strength reduction based on linear OA(4¹⁵⁶, 210, F₄, 74) (dual of [210, 54, 75]-code), using

concatenation of two codes [i] based on
1. linear OA(64²⁴, 42, F₆₄, 24) (dual of [42, 18, 25]-code or 42-arc in PG(23,64)), using
  - discarding factors / shortening the dual code based on linear OA(64²⁴, 64, F₆₄, 24) (dual of [64, 40, 25]-code or 64-arc in PG(23,64)), using
    - Reedâ€“Solomon code RS(40,64) [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(4¹⁵⁵, 209, F₄, 72) (dual of [209, 54, 73]-code)	[i]	Truncation
2	Linear OOA(4¹⁵⁶, 105, F₄, 2, 73) (dual of [(105, 2), 54, 74]-NRT-code)	[i]	OOA Folding
3	Linear OOA(4¹⁵⁶, 70, F₄, 3, 73) (dual of [(70, 3), 54, 74]-NRT-code)	[i]	OOA Folding