MinT - Information on Result #2254986

Information on Result #2254986

Linear OA(16¹⁰⁶, 133, F₁₆, 67) (dual of [133, 27, 68]-code), using 2 times truncation based on linear OA(16¹⁰⁸, 135, F₁₆, 69) (dual of [135, 27, 70]-code), using

generalized (u,Â u+v)-construction [i] based on
1. 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]
2. linear OA(16⁴, 9, F₁₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,16)) (see above)
3. 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]
4. linear OA(16⁵, 9, F₁₆, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,16)) (see above)
5. 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]
6. linear OA(16⁶, 9, F₁₆, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,16)) (see above)
7. 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]
8. 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]
9. 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]
10. linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
11. linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
12. linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
13. linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
14. linear OA(16⁹, 9, F₁₆, 9) (dual of [9, 0, 10]-code or 9-arc in PG(8,16)) (see above)
15. 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

None.