Zobrazeno 1 - 10
of 57 493
pro vyhledávání: '"Codewords"'
In this paper, we tie together two well studied topics related to finite Desarguesian affine and projective planes. The first topic concerns directions determined by a set, or even a multiset, of points in an affine plane. The second topic concerns t
Externí odkaz:
http://arxiv.org/abs/2411.19201
In this paper, we present a deterministic algorithm to count the low-weight codewords of punctured and shortened pure and pre-transformed polar codes. The method first evaluates the weight properties of punctured/shortened polar cosets. Then, a metho
Externí odkaz:
http://arxiv.org/abs/2411.05433
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that connects
Externí odkaz:
http://arxiv.org/abs/2407.18398
Autor:
Özen, İbrahim1 iozen@marmara.edu.tr
Publikováno v:
European Journal of Pure & Applied Mathematics. Oct2024, Vol. 17 Issue 4, p4225-4237. 13p.
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this work, we pro
Externí odkaz:
http://arxiv.org/abs/2311.17774
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
On the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes
Autor:
Ghorpade, Sudhir R., Ludhani, Rati
We give an alternative proof of the formula for the minimum distance of a projective Reed-Muller code of an arbitrary order. It leads to a complete characterization of the minimum weight codewords of a projective Reed-Muller code. This is then used t
Externí odkaz:
http://arxiv.org/abs/2309.10196
The weight distribution of error correction codes is a critical determinant of their error-correcting performance, making enumeration of utmost importance. In the case of polar codes, the minimum weight $\wm$ (which is equal to minimum distance $d$)
Externí odkaz:
http://arxiv.org/abs/2305.02921
Autor:
Adriaensen, Sam, Denaux, Lins
The $p$-ary linear code $\mathcal C_{k}(n,q)$ is defined as the row space of the incidence matrix $A$ of $k$-spaces and points of $\text{PG}(n,q)$. It is known that if $q$ is square, a codeword of weight $q^k\sqrt{q}+\mathcal O \left( q^{k-1} \right)
Externí odkaz:
http://arxiv.org/abs/2309.00490