MinT - Information on Result #1708319

Information on Result #1708319

Linear OOA(2⁶², 1154, F₂, 15, 11) (dual of [(1154, 15), 17248, 12]-NRT-code), using OOA stacking with additional row based on linear OOA(2⁶², 1155, F₂, 5, 11) (dual of [(1155, 5), 5713, 12]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁶², 1155, F₂, 3, 11) (dual of [(1155, 3), 3403, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁶², 1370, F₂, 3, 11) (dual of [(1370, 3), 4048, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁶², 4110, F₂, 11) (dual of [4110, 4048, 12]-code), using
    - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
      1. linear OA(2⁶¹, 4096, F₂, 11) (dual of [4096, 4035, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(2⁴⁹, 4096, F₂, 9) (dual of [4096, 4047, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(2¹³, 14, F₂, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
        dual of repetition code with length 14 [i]
      4. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (51, 62, 1154)-net over F₂	[i]		Net Defined by OOA