On Self-dual Codes over Z 16

Nagata, Kiyoshi; Nemenzo, Fidel R.; Wada, Hideo

doi:10.1007/978-3-642-02181-7_12

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…To find a generator matrix of an (extremal or optimal) free self-dual code C over Z 16 with Res( C ) = C, we use a generator matrix G of an (extremal or optimal) free self-dual code over Z 8 , where C is an (extremal or optimal) binary Type II code. We use the following notation for Theorem 3.8 and Algorithm 2.…”

Section: Casementioning

confidence: 99%

“…Harada [10] suggested a method for construction of extremal Type II codes over Z 4 by using binary Type II codes with respect to the Euclidean weight. Moreover, Nagata et al [16] found the mass formula of self-dual codes over Z 16 .…”

Section: Introductionmentioning

confidence: 98%

“…The main goal of this paper is constructing (extremal or optimal) free self-dual codes over Z 8 and Z 16 . A code is defined to be extremal if its minimum distance meets the largest of the applicable bound.…”

Section: Introductionmentioning

confidence: 99%

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Construction of extremal self-dual codes over $${\mathbb {Z}}_{8}$$ Z 8 and $${\mathbb {Z}}_{16}$$ Z 16

Kim

Lee

2015

Des. Codes Cryptogr.

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We present a method of constructing free self-dual codes over Z 8 and Z 16 which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over Z 2 m can be found from a binary (extremal or optimal) Type II code for any positive integer m ≥ 2. We find explicit algorithms for construction of self-dual codes over Z 8 and Z 16 . Our construction method is basically a lifting method. Furthermore, we find an upper bound of minimum Hamming weights of free self-dual codes over Z 2 m . By using our explicit algorithms, we construct extremal free self-dual codes over Z 8 and Z 16 up to lengths 40.

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Section: Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Construction of extremal self-dual codes over $${\mathbb {Z}}_{8}$$ Z 8 and $${\mathbb {Z}}_{16}$$ Z 16

Kim

Lee

2015

Des. Codes Cryptogr.

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“…See [10] for quadratic residue codes over Z 16 and [15] for codes over Z 9 for example. However it is generally difficult to give general formulas for such generators.…”

Section: Quadratic Residue Codes Over Z 3 Ementioning

confidence: 99%