MinT - Information on Result #2239614

Information on Result #2239614

Linear OA(4¹²³, 168, F₄, 57) (dual of [168, 45, 58]-code), using 2 times truncation based on linear OA(4¹²⁵, 170, F₄, 59) (dual of [170, 45, 60]-code), using

concatenation of two codes [i] based on
1. linear OA(64¹⁹, 34, F₆₄, 19) (dual of [34, 15, 20]-code or 34-arc in PG(18,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁹, 64, F₆₄, 19) (dual of [64, 45, 20]-code or 64-arc in PG(18,64)), using
    - Reedâ€“Solomon code RS(45,64) [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(4¹²³, 84, F₄, 2, 57) (dual of [(84, 2), 45, 58]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4¹²³, 56, F₄, 3, 57) (dual of [(56, 3), 45, 58]-NRT-code)	[i]		OOA Folding