MinT - Information on Result #637231

Information on Result #637231

Linear OA(4⁹⁹, 120, F₄, 55) (dual of [120, 21, 56]-code), using concatenation of two codes based on

linear OA(64¹³, 20, F₆₄, 13) (dual of [20, 7, 14]-code or 20-arc in PG(12,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹³, 64, F₆₄, 13) (dual of [64, 51, 14]-code or 64-arc in PG(12,64)), using
  - Reedâ€“Solomon code RS(51,64) [i]
linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- hyperoval in PG(2,Â 4) [i]
- the Hexacode [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 OA(4⁹⁹, 120, F₄, 54) (dual of [120, 21, 55]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁰⁰, 121, F₄, 55) (dual of [121, 21, 56]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4⁹⁸, 119, F₄, 54) (dual of [119, 21, 55]-code)	[i]		Truncation
4	Linear OA(4⁹⁷, 118, F₄, 53) (dual of [118, 21, 54]-code)	[i]
5	Linear OA(4⁹⁶, 117, F₄, 52) (dual of [117, 21, 53]-code)	[i]
6	Linear OA(4⁹⁵, 116, F₄, 51) (dual of [116, 21, 52]-code)	[i]
7	Linear OOA(4⁹⁹, 60, F₄, 2, 55) (dual of [(60, 2), 21, 56]-NRT-code)	[i]		OOA Folding
8	Linear OOA(4⁹⁹, 40, F₄, 3, 55) (dual of [(40, 3), 21, 56]-NRT-code)	[i]		OOA Folding