On even codes

Quebbemann, Heinz-Georg

doi:10.1016/0012-365x(91)90410-4

Cited by 9 publications

(15 citation statements)

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“…For further details about this first section see [12]. In [15] Quebbemann defines the notion of an even code over the field k := F 2 f as follows. A code C ≤ k N is called even if It is easy to see that even codes are self-orthogonal with respect to the usual bilinear form…”

Section: Ii) If R Is a Finite Quasi-chain Ring Then Inv(c(ρ)) Is Spanmentioning

confidence: 99%

Codes and invariant theory

Nebe¹,

Rains²,

Sloane³

2004

Mathematische Nachrichten

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The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book. However, the theorem can be stated and applied without using category theory, and we illustrate it here by applying it to generalized doubly-even codes over fields of characteristic 2, doubly-even codes over Z/2 f Z, and self-dual codes over the noncommutative ring F q + F q u, where u 2 = 0..

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Section: Ii) If R Is a Finite Quasi-chain Ring Then Inv(c(ρ)) Is Spanmentioning

confidence: 99%

Codes and invariant theory

Nebe¹,

Rains²,

Sloane³

2004

Mathematische Nachrichten

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“…q E II Same as q E I but additionally assuming that the codes are generalized doubly even as defined in [10]. Then the associated Clifford-Weil group is C m (q E II ) ∼ = Z 8 Y2 1+2mf .…”

Section: Codes Over Finite Fieldsmentioning

confidence: 98%

Finite Weil representations and associated Hecke algebras

Nebe

2009

Journal of Number Theory

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An algebra H(G m ) of double cosets is constructed for every finite Weil representation G m . For the Clifford-Weil groups G m = C m (ρ) associated to some classical Type ρ of selfdual codes over a finite field, this algebra is shown to be commutative. Then the eigenspace decomposition of H(C m (ρ)) acting on the space of degree N invariants of C m (ρ) may be obtained from the kernels of powers of the coding theory analogue of the Siegel Φ-operator.

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“…• 2n = 48. There is a unique Type II [48, 24,12] code, an optimal rate one-half code of that length. • 2n = 50.…”

Section: Cis Codes With Record Distancesmentioning

confidence: 99%

A New Class of Codes for Boolean Masking of Cryptographic Computations

Carlet¹,

Gaborit²,

Kim³

et al. 2012

IEEE Trans. Inform. Theory

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We introduce a new class of rate one-half binary codes: complementary information set codes. A binary linear code of length 2n and dimension n is called a complementary information set code (CIS code for short) if it has two disjoint information sets. This class of codes contains self-dual codes as a subclass. It is connected to graph correlation immune Boolean functions of use in the security of hardware implementations of cryptographic primitives. Such codes permit to improve the cost of masking cryptographic algorithms against side channel attacks. In this paper we investigate this new class of codes: we give optimal or best known CIS codes of length < 132. We derive general constructions based on cyclic codes and on double circulant codes. We derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all be classified in small lengths ≤ 12 by the building up construction. Some nonlinear permutations are constructed by using Z 4 -codes, based on the notion of dual distance of an unrestricted code.Keywords: cyclic codes, self-dual codes, dual distance, double circulant codes, Z 4 -codes I. INTRODUCTION Since the seminal work of P. Kocher [18], [19], it is known that the physical implementation of cryptosystems on devices such as smart cards leaks information which can be used in differential power analysis or in other kinds of side channel attacks. These attacks can be devastating if proper counter-measures are not included in the implementation. A kind of counter-measure, which is suitable for both hardware and software cryptographic implementations and does not rely on specific hardware properties is the following. It consists in applying a kind of secret sharing method, changing the variable representation (say x) into randomized shares m 1 , m 2 , . . . , m d+1 called masks such that x = m 1 + m 2 + · · · + m d+1 where + is a group operation -in practice, the XOR. Since the difficulty of performing an attack of order d (involving d + 1 shares) increases exponentially with d, it was believed until recently that for increasing the resistance to attacks, new masks have to be added, thereby increasing the order of the countermeasure, see [25]. But in these schemes, the profusion of masks implies a heavy load on the true random number generator, which significantly degrades the performance of the device. Moreover, the solution in [25] bases itself on a mask refreshing operation for which no secure implementation has been detailed so far. Now, it is shown in [21] that another option consists in encoding some of the masks, which is much less costly than adding fresh masks. At the order 1, this consists in representing x by the ordered pair (F (m), x + m), where F is a well

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On even codes

Cited by 9 publications

References 1 publication

Codes and invariant theory

Codes and invariant theory

Finite Weil representations and associated Hecke algebras

A New Class of Codes for Boolean Masking of Cryptographic Computations

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