MinT - Information on Result #2274040

Information on Result #2274040

Linear OA(4¹¹⁴, 156, F₄, 53) (dual of [156, 42, 54]-code), using 1 times code embedding in larger space based on linear OA(4¹¹³, 155, F₄, 53) (dual of [155, 42, 54]-code), using

concatenation of two codes [i] based on
1. linear OA(64¹⁷, 31, F₆₄, 17) (dual of [31, 14, 18]-code or 31-arc in PG(16,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁷, 64, F₆₄, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), using
    - Reedâ€“Solomon code RS(47,64) [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(4¹¹⁴, 78, F₄, 2, 53) (dual of [(78, 2), 42, 54]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4¹¹⁴, 52, F₄, 3, 53) (dual of [(52, 3), 42, 54]-NRT-code)	[i]		OOA Folding