MinT - Information on Result #634934

Information on Result #634934

Linear OA(4⁶³, 75, F₄, 39) (dual of [75, 12, 40]-code), using concatenation of two codes based on

linear OA(16⁹, 15, F₁₆, 9) (dual of [15, 6, 10]-code or 15-arc in PG(8,16)), using
- discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
  - Reedâ€“Solomon code RS(7,16) [i]
linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reedâ€“Solomon code RS_e(2,4) [i]
- Simplex code S(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 OA(4⁶³, 75, F₄, 38) (dual of [75, 12, 39]-code)	[i]		Strength Reduction
2	Linear OA(4⁶³, 75, F₄, 37) (dual of [75, 12, 38]-code)	[i]		Strength Reduction
3	Linear OA(4⁶², 74, F₄, 38) (dual of [74, 12, 39]-code)	[i]		Truncation
4	Linear OA(4⁶¹, 73, F₄, 37) (dual of [73, 12, 38]-code)	[i]
5	Linear OA(4⁶⁰, 72, F₄, 36) (dual of [72, 12, 37]-code)	[i]
6	Linear OA(4⁵⁹, 71, F₄, 35) (dual of [71, 12, 36]-code)	[i]
7	Linear OA(4⁵⁸, 70, F₄, 34) (dual of [70, 12, 35]-code)	[i]
8	Linear OA(2¹⁹⁸, 216, F₂, 79) (dual of [216, 18, 80]-code)	[i]		Concatenation of Two Codes
9	Linear OOA(4⁶³, 37, F₄, 2, 39) (dual of [(37, 2), 11, 40]-NRT-code)	[i]		OOA Folding
10	Linear OOA(4⁶³, 25, F₄, 3, 39) (dual of [(25, 3), 12, 40]-NRT-code)	[i]		OOA Folding