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A Gleason Formula for Ozeki Polynomials

2002
*
Journal of combinatorial theory. Series A
*

ACKNOWLEDGMENTS The authors thank Don Zagier

doi:10.1006/jcta.2001.3226
fatcat:7t7r465hinh6tbmo6nejrgwfom
*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*. ...##
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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*. ...##
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Page 6101 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
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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. ...##
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Construction of divisible formal weight enumerators and extremal polynomials not satisfying the Riemann hypothesis
[article]

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. ...

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

2011
*
arXiv
*
pre-print

Namely, we use the finite-dimensional representation theory of sl_2 to derive

arXiv:1111.2392v1
fatcat:lgv7mqugvneqjbfqbulgcg4r6u
*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. ...##
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Self-Dual Codes
[article]

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,

arXiv:math/0208001v1
fatcat:vgqbfd4h6faehj34upylbqw3km
*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. ...##
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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. ...##
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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). ...##
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Page 2953 of Mathematical Reviews Vol. , Issue Index
[page]

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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*. ...##
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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. ...##
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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. ...