MinT - Information on Result #1191354

Information on Result #1191354

Digital (88, 98, 2812368)-net over F₈, using net defined by OOA based on linear OOA(8⁹⁸, 2812368, F₈, 15, 10) (dual of [(2812368, 15), 42185422, 11]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁹⁸, 5624737, F₈, 3, 10) (dual of [(5624737, 3), 16874113, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8²⁴, 32335, F₈, 3, 5) (dual of [(32335, 3), 96981, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(8²⁴, 32336, F₈, 2, 5) (dual of [(32336, 2), 64648, 6]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(8⁰, 4042, F₈, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8⁰, s, F₈, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(8⁰, 4042, F₈, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code) (see above)
        linear OOA(8⁰, 4042, F₈, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code) (see above)
        linear OOA(8¹, 4042, F₈, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(8¹, 4042, F₈, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code) (see above)
        linear OOA(8¹, 4042, F₈, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code) (see above)
        linear OOA(8⁵, 4042, F₈, 2, 2) (dual of [(4042, 2), 8079, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8⁵, 4681, F₈, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
        appending kth column [i] based on linear OA(8⁵, 4681, F₈, 2) (dual of [4681, 4676, 3]-code), using
        Hamming code H(5,8) [i]
        linear OOA(8¹⁶, 4042, F₈, 2, 5) (dual of [(4042, 2), 8068, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(8², 9, F₈, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;16,8) [i]
        linear OOA(8¹⁴, 4033, F₈, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
        trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(8⁷⁴, 5592402, F₈, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
    - trace code [i] based on linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.