Extending self-orthogonal codes

Bassa, Alp; Tutaş, Nesrin

doi:10.3906/mat-1905-103

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Macwilliams Identity1

Now Let Us Define1

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2021

2023

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Cited by 2 publications

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“…where α i ∈ F p , and χ(α) := ζ α 0 p , where ζ p is the primitive p-th root e 2πi/ p of unity, and α 0 is given by (1).…”

Section: Macwilliams Identitymentioning

confidence: 99%

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Average of complete joint weight enumerators and self-dual codes

Chakraborty

Miezaki

2021

Des. Codes Cryptogr.

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In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length n over F q and Z k in terms of the compositions of n and their distributions in the codes. We also obtain a generalization of the representation for the average of g-fold complete joint weight enumerators of codes over F q and Z k . Finally, the average of intersection numbers of a pair of Type III (resp. Type IV) codes, and its second moment are found.

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“…where α i ∈ F p , and χ(α) := ζ α 0 p , where ζ p is the primitive p-th root e 2πi/ p of unity, and α 0 is given by (1).…”

Section: Macwilliams Identitymentioning

confidence: 99%

“…Let C ⊆ F n 3 be a self-orthogonal code of dimension k. We denote by N III n,k the number of Type III codes over F 3 of length n containing C . Then from [1] we have…”

Section: Now Let Us Definementioning

confidence: 99%

Average of complete joint weight enumerators and self-dual codes

Chakraborty

Miezaki

2021

Des. Codes Cryptogr.

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Narain CFTs from qudit stabilizer codes

2023

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We construct a discrete subset of Narain CFTs from quantum stabilizer codes with qudit (including qubit) systems whose dimension is a prime number. Our construction exploits three important relations. The first relation is between qudit stabilizer codes and classical codes. The second is between classical codes and Lorentzian lattices. The third is between Lorentzian lattices and Narain CFTs. In particular, we study qudit Calderbank-Shor-Steane (CSS) codes as a special class of qudit stabilizer codes and the ensembles of the Narain code CFTs constructed from CSS codes. We obtain exact results for the averaged partition functions over the ensembles and discuss their implications for holographic duality.

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Extending self-orthogonal codes

Abstract: In this short note we give an exact count for the number of self-dual codes over a finite field Fq of odd characteristic containing a given self-orthogonal code. This generalizes an analogous result of MacWilliams, Sloane, and Thompson over the field F2 to arbitrary odd finite fields Fq .

Cited by 2 publications

References 4 publications

Average of complete joint weight enumerators and self-dual codes

Average of complete joint weight enumerators and self-dual codes

Narain CFTs from qudit stabilizer codes

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