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## Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$

#### Augustine İ. MUSUKWA [1] , Kondwani MAGAMBA [2] , John A. RYAN [3]

Let $n$ be an odd prime and $m>1$ be a positive integer. We produce an upper bound on the number of inequivalent extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$. Some examples are given to illustrate our results.
Goppa codes, Extended codes, Irreducible Goppa codes, Equivalent codes
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Subjects Engineering Articles Orcid: 0000-0001-8792-6954Author: Augustine İ. MUSUKWA Orcid: 0000-0003-4025-9802Author: Kondwani MAGAMBA Author: John A. RYAN Publication Date : September 15, 2017
 Bibtex @research article { jacodesmath327368, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2017}, volume = {4}, pages = {235 - 246}, doi = {10.13069/jacodesmath.327368}, title = {Enumeration of extended irreducible binary Goppa codes of degree \$2\^\{m\}\$ and length \$2\^\{n\}+1\$}, key = {cite}, author = {Musukwa, Augustine İ. and Magamba, Kondwani and Ryan, John A.} } APA Musukwa, A , Magamba, K , Ryan, J . (2017). Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$ . Journal of Algebra Combinatorics Discrete Structures and Applications , 4 (3) , 235-246 . DOI: 10.13069/jacodesmath.327368 MLA Musukwa, A , Magamba, K , Ryan, J . "Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$" . Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 235-246 Chicago Musukwa, A , Magamba, K , Ryan, J . "Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 235-246 RIS TY - JOUR T1 - Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$ AU - Augustine İ. Musukwa , Kondwani Magamba , John A. Ryan Y1 - 2017 PY - 2017 N1 - doi: 10.13069/jacodesmath.327368 DO - 10.13069/jacodesmath.327368 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 235 EP - 246 VL - 4 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.327368 UR - https://doi.org/10.13069/jacodesmath.327368 Y2 - 2016 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$ %A Augustine İ. Musukwa , Kondwani Magamba , John A. Ryan %T Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$ %D 2017 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 3 %R doi: 10.13069/jacodesmath.327368 %U 10.13069/jacodesmath.327368 ISNAD Musukwa, Augustine İ. , Magamba, Kondwani , Ryan, John A. . "Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$". Journal of Algebra Combinatorics Discrete Structures and Applications 4 / 3 (September 2017): 235-246 . https://doi.org/10.13069/jacodesmath.327368 AMA Musukwa A , Magamba K , Ryan J . Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(3): 235-246. Vancouver Musukwa A , Magamba K , Ryan J . Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(3): 235-246.

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