MinT - Information on Result #1013922

Information on Result #1013922

Linear OOA(7⁸⁶, 274532, F₇, 3, 13) (dual of [(274532, 3), 823510, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁷, 13, F₇, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F₇, using
  - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁷⁹, 274519, F₇, 3, 13) (dual of [(274519, 3), 823478, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁷⁹, 823557, F₇, 13) (dual of [823557, 823478, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁷⁹, 823558, F₇, 13) (dual of [823558, 823479, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(7⁷⁸, 823543, F₇, 13) (dual of [823543, 823465, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(7⁶⁴, 823543, F₇, 11) (dual of [823543, 823479, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(7¹, 15, F₇, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁸⁶, 137265, F₇, 15, 13) (dual of [(137265, 15), 2058889, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row