MinT - Information on Result #664557

Information on Result #664557

Linear OA(16¹⁰⁸, 135, F₁₆, 69) (dual of [135, 27, 70]-code), using generalized (u,Â u+v)-construction based on

linear OA(16⁴, 9, F₁₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,16)), using
- discarding factors / shortening the dual code based on linear OA(16⁴, 16, F₁₆, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
  - Reedâ€“Solomon code RS(12,16) [i]
linear OA(16⁴, 9, F₁₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,16)) (see above)
linear OA(16⁵, 9, F₁₆, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,16)), using
- discarding factors / shortening the dual code based on linear OA(16⁵, 16, F₁₆, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
  - Reedâ€“Solomon code RS(11,16) [i]
linear OA(16⁵, 9, F₁₆, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,16)) (see above)
linear OA(16⁶, 9, F₁₆, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,16)), using
- discarding factors / shortening the dual code based on linear OA(16⁶, 16, F₁₆, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)), using
  - Reedâ€“Solomon code RS(10,16) [i]
linear OA(16⁶, 9, F₁₆, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,16)) (see above)
linear OA(16⁷, 9, F₁₆, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,16)), using
- discarding factors / shortening the dual code based on linear OA(16⁷, 16, F₁₆, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
  - Reedâ€“Solomon code RS(9,16) [i]
linear OA(16⁸, 9, F₁₆, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,16)), using
- dual of repetition code with length 9 [i]
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)), using
- complete OA / dual of code with only one code word [i]
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(16¹⁰⁷, 134, F₁₆, 68) (dual of [134, 27, 69]-code)	[i]		Truncation
2	Linear OA(16¹⁰⁶, 133, F₁₆, 67) (dual of [133, 27, 68]-code)	[i]		Truncation