Generalizations of Gleason's theorem on weight enumerators of self-dual codes

1972 ◽  
Vol 18 (6) ◽  
pp. 794-805 ◽  
Author(s):  
F. MacWilliams ◽  
C. Mallows ◽  
N. Sloane
Keyword(s):  
Dual Codes ◽  
Weight Enumerators ◽  
Gleason's Theorem ◽  
Gleason’S Theorem

Gleason's theorem on self-dual codes

1972 ◽  
Vol 18 (3) ◽  
pp. 409-414 ◽  
Author(s):  
E. Berlekamp ◽  
F. MacWilliams ◽  
N. Sloane
Keyword(s):  
Dual Codes ◽  
Gleason's Theorem ◽  
Gleason’S Theorem

The (virtual) conceptual necessity of quantum probabilities in cognitive psychology

2013 ◽  
Vol 36 (3) ◽  
pp. 280-281
Author(s):  
Reinhard Blutner ◽  
Peter beim Graben
Keyword(s):  
Cognitive Psychology ◽  
Orthomodular Lattice ◽  
The State ◽  
Input State ◽  
Cognitive Tests ◽  
Quantum Probabilities ◽  
Conceptual Necessity ◽  
Gleason's Theorem ◽  
Gleason’S Theorem ◽  
General Conditions

AbstractWe propose a way in which Pothos & Busemeyer (P&B) could strengthen their position. Taking a dynamic stance, we consider cognitive tests as functions that transfer a given input state into the state after testing. Under very general conditions, it can be shown that testable properties in cognition form an orthomodular lattice. Gleason's theorem then yields the conceptual necessity of quantum probabilities (QP).

scholarly journals Extremal binary self-dual codes of lengths 64 and 66 from four-circulant constructions over F2+uF2

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 937-945 ◽  
Author(s):  
Suat Karadeniz ◽  
Bahattin Yildiz ◽  
Nuh Aydin
Keyword(s):  
Dual Codes ◽  
Weight Enumerators ◽  
Extension Method ◽  
Extremal Codes ◽  
New Codes ◽  
First Time

A classification of all four-circulant extremal codes of length 32 over F2 + uF2 is done by using four-circulant binary self-dual codes of length 32 of minimum weights 6 and 8. As Gray images of these codes, a substantial number of extremal binary self-dual codes of length 64 are obtained. In particular a new code with ?=80 in W64,2 is found. Then applying an extension method from the literature to extremal self-dual codes of length 64, we have found many extremal binary self-dual codes of length 66. Among those, five of them are new codes in the sense that codes with these weight enumerators are constructed for the first time. These codes have the values ?=1, 30, 34, 84, 94 in W66,1.

Weight enumerators of reducible cyclic codes and their dual codes

2019 ◽  
Vol 342 (3) ◽  
pp. 671-682 ◽  
Author(s):  
Yansheng Wu ◽  
Qin Yue ◽  
Xiaomeng Zhu ◽  
Shudi Yang
Keyword(s):  
Cyclic Codes ◽  
Dual Codes ◽  
Weight Enumerators
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