MinT - Information on Result #1698720

Information on Result #1698720

Linear OOA(2¹⁴², 26219, F₂, 8, 17) (dual of [(26219, 8), 209610, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴², 26219, F₂, 5, 17) (dual of [(26219, 5), 130953, 18]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁴², 131095, F₂, 17) (dual of [131095, 130953, 18]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2¹³⁸, 131091, F₂, 17) (dual of [131091, 130953, 18]-code), using
  - constructionÂ X4 applied to C_e(16) âŠ‚ C_e(14) [i] based on
    1. linear OA(2¹³⁷, 131072, F₂, 17) (dual of [131072, 130935, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(2¹²⁰, 131072, F₂, 15) (dual of [131072, 130952, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(2¹⁸, 19, F₂, 17) (dual of [19, 1, 18]-code), using
      - strength reduction [i] based on linear OA(2¹⁸, 19, F₂, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
        dual of repetition code with length 19 [i]
    4. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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: 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(2¹⁴², 26218, F₂, 24, 17) (dual of [(26218, 24), 629090, 18]-NRT-code)	[i]		OOA Stacking with Additional Row