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- Wolfgang Willems
- IEEE Trans. Information Theory
- 2002

- Stefka Bouyuklieva, E. A. O'Brien, Wolfgang Willems
- IEEE Trans. Information Theory
- 2006

We prove that the automorphism group of a putative binary self-dual doubly-even [72,36,16] code is solvable. Moreover, its order is 5, 7, 10, 14, 56, or a divisor of 72.

Let p be a prime with p≡3 (mod 4), let n be an odd natural number and let . Consider the crosscorrelation funtion C d (t)=∑ i =1 pn−1 ζ ai − adi−t where ζ≠1 is a complex p-th root of unity and (a i ) is a maximal linear shift register sequence. In 7 the bound has been computed for p = 3. In this note we generalize this to for p≥ 3. Furthermore we giv an… (More)

- Andreas Faldum, Julio Lafuente, Gustavo Ochoa, Wolfgang Willems
- Des. Codes Cryptography
- 2006

- Stefka Bouyuklieva, Anton Malevich, Wolfgang Willems
- Adv. in Math. of Comm.
- 2011

- Stefka Bouyuklieva, Wolfgang Willems
- IEEE Transactions on Information Theory
- 2012

In this paper, extremal singly even self-dual codes with minimal shadow are investigated. Nonexistence of such codes for particular parameters is proved. By a result of Rains, the length of extremal singly even self-dual codes is bounded. Explicit bounds are given in case the shadow is minimal.

- Hans Dobbertin, Donald Mills, Eva Nuria Müller, Alexander Pott, Wolfgang Willems
- Discrete Mathematics
- 2003

- Conchita Martínez-Pérez, Wolfgang Willems
- IEEE Transactions on Information Theory
- 2004

Using representation theoretical methods we investigate self-dual group codes and their extensions in characteristic 2. We prove that the existence of a self-dual extended group code heavily depends on a particular structure of the group algebra KG which can be checked by an easy-to-handle criteria in elementary number theory. Surprisingly, in the binary… (More)

- Iliya Bouyukliev, Veerle Fack, Wolfgang Willems, Joost Winne
- Des. Codes Cryptography
- 2006

- E. A. O'Brien, Wolfgang Willems
- IEEE Trans. Information Theory
- 2011

— We prove that the automor-phism group of a binary self-dual doubly-even [72, 36, 16] code has order 5, 7, 10, 14 or d where d divides 18 or 24, or it is A4 × C3.