MinT - Information on Result #806706

Information on Result #806706

Linear OOA(2²³⁴, 1048588, F₂, 2, 22) (dual of [(1048588, 2), 2096942, 23]-NRT-code), using OOA 2-folding based on linear OA(2²³⁴, 2097176, F₂, 22) (dual of [2097176, 2096942, 23]-code), using

strength reduction [i] based on linear OA(2²³⁴, 2097176, F₂, 23) (dual of [2097176, 2096942, 24]-code), using
- adding a parity check bit [i] based on linear OA(2²³³, 2097175, F₂, 22) (dual of [2097175, 2096942, 23]-code), using
  - constructionÂ X4 applied to C([0,22]) âŠ‚ C([1,20]) [i] based on
    1. linear OA(2²³², 2097151, F₂, 23) (dual of [2097151, 2096919, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    2. linear OA(2²¹⁰, 2097151, F₂, 20) (dual of [2097151, 2096941, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(2²³, 24, F₂, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
      - dual of repetition code with length 24 [i]
    4. linear OA(2¹, 24, F₂, 1) (dual of [24, 23, 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(2²³⁶, 1048589, F₂, 2, 22) (dual of [(1048589, 2), 2096942, 23]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(2²³⁵, 1048588, F₂, 2, 22) (dual of [(1048588, 2), 2096941, 23]-NRT-code)	[i]		OOA Duplication