MinT - Information on Result #1150897

Information on Result #1150897

Linear OOA(2¹⁰⁶, 4683, F₂, 7, 14) (dual of [(4683, 7), 32675, 15]-NRT-code), using OOA 7-folding based on linear OA(2¹⁰⁶, 32781, F₂, 14) (dual of [32781, 32675, 15]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁰⁶, 32784, F₂, 14) (dual of [32784, 32678, 15]-code), using
- 1 times truncation [i] based on linear OA(2¹⁰⁷, 32785, F₂, 15) (dual of [32785, 32678, 16]-code), using
  - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
    1. linear OA(2¹⁰⁶, 32768, F₂, 15) (dual of [32768, 32662, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
      - strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
    4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁰⁸, 4683, F₂, 7, 14) (dual of [(4683, 7), 32673, 15]-NRT-code)	[i]		OOA Duplication