A concatenation construction for propelinear perfect codes from regular subgroups of GA (r,2)
نویسندگان
چکیده
منابع مشابه
A generalized concatenation construction for q-ary 1-perfect codes
We consider perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). In this paper, a generalized concatenation construction for q-ary 1-perfect codes is presented that allows us to construct q-ary 1-perfect codes of length (q − 1)nm + n +m from the given q-ary 1-perfect codes of length n = (q1 − 1)/(q − 1) and m = (q2 − 1)/(q − 1), where s1, s2 are ...
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It is proven that for any numbers n = 2 m − 1, m ≥ 4 and r, such that n − log(n + 1) ≤ r ≤ n excluding n = r = 63, n = 127, r ∈ {126, 127} and n = r = 2047 there exists a propelinear perfect binary code of length n and rank r.
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The paper proves that there exists an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov (2007) are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the ...
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In this paper from q-ary perfect codes a new completely regular q-ary codes are constructed. In particular two new ternary completely regular codes are obtained from the ternary Golay [11,6,5] code and new families of q-ary completely regular codes are obtained from q-ary 1-perfect codes.
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A class of binary group codes is investigated. These codes are the propelinear codes, deened over the Hamming metric space F n , F = f0; 1g, with a group structure. Generally, they are neither abelian nor translation invariant codes but they have good algebraic and com-binatorial properties. Linear codes and Z 4-linear codes can be seen as a subclass of prope-linear codes. Exactly, it is shown ...
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ژورنال
عنوان ژورنال: Sibirskie Elektronnye Matematicheskie Izvestiya
سال: 2019
ISSN: 1813-3304
DOI: 10.33048/semi.2019.16.119