On self-dual negacirculant codes of index two and four

Shi, Minjia; Qian, Liqin; Solé, Patrick

doi:10.1007/s10623-017-0455-0

Cited by 61 publications

(18 citation statements)

References 11 publications

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“…7]. This generalizes the asymptotic properties of self-dual double-circulant codes [3], and of self-dual negacirculant codes [4,24]. The proof is restricted to F 2 where we can show that an infinite family of irreducible trinomials exists.…”

Section: Introductionmentioning

confidence: 55%

Construction of isodual codes from polycirculant matrices

Shi

Solé

2020

Des. Codes Cryptogr.

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Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over F 2 in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over F 2 , we show that binary double polycirculant codes are asymptotically good.

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Section: Introductionmentioning

confidence: 55%

Construction of isodual codes from polycirculant matrices

Shi

Solé

2020

Des. Codes Cryptogr.

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“…Proof By the Gray map over R k , we see that the Gray image of the several families of codes of length 2m are linear codes of length 2mp k−1 . Combining Lemmas 3.4, 4.1, 4.2, 4.3, 4.4 and Theorem 3.9, the result follows by the same method as Theorem 5.2 in [20], so we omit the detailed proof here.…”

Section: Case (2) In Theorem 39mentioning

confidence: 89%

On self-dual and LCD quasi-twisted codes of index two over a special chain ring

Qian

Shi

Solé³

2018

Cryptogr. Commun.

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“…. , 25,28,19,30,32,33,34,36,37,38,40,41,42,44,45,48,50,51,52,56,58,64,72,80,88,96,104,108,112,114,118…”

Section: Constructions Coming From Dmentioning

confidence: 99%

Double bordered constructions of self-dual codes from group rings over Frobenius rings

et al. 2020

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In this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings F 2 + uF 2 and F 4 + uF 4. We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables. Keywords Group rings • Self-dual codes • Codes over rings • Extremal codes • Bordered constructions Mathematics Subject Classification (2010) 94B05 • 94B15 This research was supported by the London Mathematical Society (International Short Visits-Scheme 5).

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On self-dual negacirculant codes of index two and four

Cited by 61 publications

References 11 publications

Construction of isodual codes from polycirculant matrices

Construction of isodual codes from polycirculant matrices

On self-dual and LCD quasi-twisted codes of index two over a special chain ring

Double bordered constructions of self-dual codes from group rings over Frobenius rings

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