MinT - Information on Result #1665111

Information on Result #1665111

Linear OOA(2¹⁵⁵, 26218, F₂, 6, 18) (dual of [(26218, 6), 157153, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁵, 26218, F₂, 5, 18) (dual of [(26218, 5), 130935, 19]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁵⁵, 131090, F₂, 18) (dual of [131090, 130935, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁵⁵, 131091, F₂, 18) (dual of [131091, 130936, 19]-code), using
  - constructionÂ X4 applied to C([0,18]) âŠ‚ C([1,16]) [i] based on
    1. linear OA(2¹⁵⁴, 131071, F₂, 19) (dual of [131071, 130917, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(2¹³⁶, 131071, F₂, 16) (dual of [131071, 130935, 17]-code), using 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]
    3. linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
      - dual of repetition code with length 20 [i]
    4. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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(2¹⁵⁶, 26218, F₂, 6, 18) (dual of [(26218, 6), 157152, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁵⁷, 26218, F₂, 6, 18) (dual of [(26218, 6), 157151, 19]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁸, 26218, F₂, 6, 18) (dual of [(26218, 6), 157150, 19]-NRT-code)	[i]