MinT - Information on Result #1179809

Information on Result #1179809

Linear OOA(2⁷⁶, 6556, F₂, 10, 10) (dual of [(6556, 10), 65484, 11]-NRT-code), using OA 5-folding and stacking based on linear OA(2⁷⁶, 32780, F₂, 10) (dual of [32780, 32704, 11]-code), using

discarding factors / shortening the dual code based on linear OA(2⁷⁶, 32784, F₂, 10) (dual of [32784, 32708, 11]-code), using
- 1 times truncation [i] based on linear OA(2⁷⁷, 32785, F₂, 11) (dual of [32785, 32708, 12]-code), using
  - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
    1. linear OA(2⁷⁶, 32768, F₂, 11) (dual of [32768, 32692, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(2⁶¹, 32768, F₂, 9) (dual of [32768, 32707, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
      - strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
    4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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: Constructive and 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 (66, 76, 6556)-net over F₂	[i]		Net Defined by OOA