MinT - Information on Result #1598994

Information on Result #1598994

Linear OOA(2²⁴¹, 2801667, F₂, 4, 16) (dual of [(2801667, 4), 11206427, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴¹, 2801667, F₂, 3, 16) (dual of [(2801667, 3), 8404760, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁷, 5466, F₂, 3, 8) (dual of [(5466, 3), 16341, 9]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁵⁷, 16398, F₂, 8) (dual of [16398, 16341, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁵⁷, 16399, F₂, 8) (dual of [16399, 16342, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁵⁸, 16400, F₂, 9) (dual of [16400, 16342, 10]-code), using
        constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
        linear OA(2⁵⁷, 16384, F₂, 9) (dual of [16384, 16327, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2⁴³, 16384, F₂, 7) (dual of [16384, 16341, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        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]
        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]
2. linear OOA(2¹⁸⁴, 2796201, F₂, 3, 16) (dual of [(2796201, 3), 8388419, 17]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(2²⁴¹, 1400833, F₂, 7, 16) (dual of [(1400833, 7), 9805590, 17]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴¹, 1400833, F₂, 8, 16) (dual of [(1400833, 8), 11206423, 17]-NRT-code)	[i]		OOA Folding