MinT - Information on Result #1696822

Information on Result #1696822

Linear OOA(2⁹⁴, 2052, F₂, 8, 15) (dual of [(2052, 8), 16322, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁹⁴, 2052, F₂, 4, 15) (dual of [(2052, 4), 8114, 16]-NRT-code), using

OOA 4-folding [i] based on linear OA(2⁹⁴, 8208, F₂, 15) (dual of [8208, 8114, 16]-code), using
- adding a parity check bit [i] based on linear OA(2⁹³, 8207, F₂, 14) (dual of [8207, 8114, 15]-code), using
  - constructionÂ X4 applied to C([0,14]) âŠ‚ C([1,12]) [i] based on
    1. linear OA(2⁹², 8191, F₂, 15) (dual of [8191, 8099, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    2. linear OA(2⁷⁸, 8191, F₂, 12) (dual of [8191, 8113, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(2¹⁵, 16, F₂, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
      - dual of repetition code with length 16 [i]
    4. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2⁹⁵, 2052, F₂, 8, 15) (dual of [(2052, 8), 16321, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2⁹⁶, 2052, F₂, 8, 15) (dual of [(2052, 8), 16320, 16]-NRT-code)	[i]
3	Linear OOA(2⁹⁷, 2052, F₂, 8, 15) (dual of [(2052, 8), 16319, 16]-NRT-code)	[i]