MinT - Information on Result #945829

Information on Result #945829

Linear OOA(2¹⁸³, 349533, F₂, 3, 18) (dual of [(349533, 3), 1048416, 19]-NRT-code), using OOA 3-folding based on linear OA(2¹⁸³, 1048599, F₂, 18) (dual of [1048599, 1048416, 19]-code), using

2 times code embedding in larger space [i] based on linear OA(2¹⁸¹, 1048597, F₂, 18) (dual of [1048597, 1048416, 19]-code), using
- 1 times truncation [i] based on linear OA(2¹⁸², 1048598, F₂, 19) (dual of [1048598, 1048416, 20]-code), using
  - constructionÂ X4 applied to C_e(18) âŠ‚ C_e(16) [i] based on
    1. linear OA(2¹⁸¹, 1048576, F₂, 19) (dual of [1048576, 1048395, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(2¹⁶¹, 1048576, F₂, 17) (dual of [1048576, 1048415, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(2²¹, 22, F₂, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
      - dual of repetition code with length 22 [i]
    4. linear OA(2¹, 22, F₂, 1) (dual of [22, 21, 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(2¹⁸⁴, 349533, F₂, 3, 18) (dual of [(349533, 3), 1048415, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁸⁵, 349533, F₂, 3, 18) (dual of [(349533, 3), 1048414, 19]-NRT-code)	[i]		OOA Duplication