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A Gleason Formula for Ozeki Polynomials

Y. Choie, P. Solé
2002 Journal of combinatorial theory. Series A  
ACKNOWLEDGMENTS The authors thank Don Zagier for helpful discussions. The second named author thanks POSTECH Math Dept for its kind hospitality.  ...  We give the analogue of the Gleason formula for a formal weight enumerator. Ozeki Polynomials Let C be a binary code of length n.  ...  If f ¥ C[w, z, x, y Gleason Formulas We shall prove the following three generalizations of the Gleason formula from weight enumerators to Ozeki polynomials.  ... 
doi:10.1006/jcta.2001.3226 fatcat:7t7r465hinh6tbmo6nejrgwfom

Page 1625 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
{For the entire collection see MR 2002k:34003. } Lev A. Borisov (Madison, WI) 2003c:1 1043 2003¢:11041 11F50 94B05 Choie, Y. (KR-POST; Pohang) ; Solé, P. A Gleason formula for Ozeki polynomials.  ...  They also compute the images of the Bannai-Ozeki map for certain polynomials.  ... 

Page 6101 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
6101 13 COMMUTATIVE RINGS AND ALGEBRAS and also a formula for the Hilbert series. Some concrete examples are then studied as an application of the above results.  ...  ) On the ring of simultaneous invariants for the Gleason-MacWilliams group.  ... 

Construction of divisible formal weight enumerators and extremal polynomials not satisfying the Riemann hypothesis [article]

Koji Chinen
2018 arXiv   pre-print
Ozeki. They form a ring of invariant polynomials which is similar to that of the weight enumerators of Type II codes.  ...  Later, the zeta functions for linear codes were discovered and their theory was developed by I. Duursma.  ...  He would like to express his appreciation to Professor Yann Bugeaud at University of Strasbourg for his hospitality and to Kindai University for giving him a chance of the program.  ... 
arXiv:1709.03380v2 fatcat:dcslftjo2fcznbluuvznecbore

Weighted Generating Functions for Type II Lattices and Codes [article]

Noam D. Elkies, Scott Duke Kominers
2011 arXiv   pre-print
Namely, we use the finite-dimensional representation theory of sl_2 to derive a decomposition theorem for the spaces of discrete homogeneous polynomials in terms of the spaces of discrete harmonic polynomials  ...  , and prove a generalized MacWilliams identity for harmonic weight enumerators.  ...  (This notation is analogous to that of Ozeki [Oze86b] for lattices.) For a doubly even code C ⊂ F n 2 , the set C 4 is called the tetrad system of C.  ... 
arXiv:1111.2392v1 fatcat:lgv7mqugvneqjbfqbulgcg4r6u

Self-Dual Codes [article]

E.M. Rains, N.J.A. Sloane
2002 arXiv   pre-print
Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration  ...  There is a comprehensive bibliography.  ...  We also thank Susan Pope for a superb typing job.  ... 
arXiv:math/0208001v1 fatcat:vgqbfd4h6faehj34upylbqw3km

Page 478 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
of simultaneous invariants for the Gleason-MacWilliams group.  ...  Asymptotic volume formulae and hyperbolic ball packing. (English summary) 2000d:30066 McGovern, William M. Errata and a new result on signs.  ... 

Page 247 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(English summary) 2003j:11049 — (with Solé, Patrick) A Gleason formula for Ozeki polynomials. (English summary ) 2003c:11041 van Diejen, J. F. (with Spiridonov, V. P.)  ...  The integral kernel in the Kuznetsov type sum formula for SU(” + 1, 1).  ... 

Page 2953 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(English summary) 2003h:94026 Choie, Youngju (with Solé, Patrick) A Gleason formula for Ozeki polynomials. (English summary) 2003c:11041 Dougherty, Steven T.  ...  Cycle index, weight enumerator, and Tutte polynomial.  ... 

Page 1887 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
(Juncheng Wei) 20600i:35051 35360 (34A34, 35B05, 35J45) Teranishi, Yasuo (with Bannai, Eiichi; Bannai, Etsuko; Ozeki, Michio) On the ring of simultaneous invariants for the Gleason-MacWilliams group.  ...  (Takashi Ichikawa) 2000f:11071 11G10 (11G30, 14H40, 14K15) — A product formula for period integrals [translation of Sigaku 47 (1995), no. 3, 224-240]. Sugaku Expositions.  ... 

Page 1965 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(Vera Pless) 2003g:94001 94-02 (11H71, 94B05) — (with Choie, Youngju) A Gleason formula for Ozeki polynomials. (English summary) J. Combin. Theory Ser. A 98 (2002), no. 1, 60-73.  ...  Solar, Muricio (with Parada, Victor; Pradenas, Lorena; Palma, Rodrigo) A hybrid algorithm for the non-guillotine cutting problem.  ...