m-th Residue Codes with Length the Product of Two Odd Primes over Finite Fields

Yuan Bo LIU, Qun Ying LIAO

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 353-370.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 353-370. DOI: 10.12386/A2022sxxb0028

m-th Residue Codes with Length the Product of Two Odd Primes over Finite Fields

  • Yuan Bo LIU, Qun Ying LIAO
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Abstract

Let q be a power of the prime, m ≥ 2 be an integer and p1, p2 be two distinct odd primes with gcd(q, p1p2) = 1 and m | gcd(p1 - 1, p2 - 1). Based on the idea of m-th residues, the present paper gives two constructions for the m-th residue code with length n = p1p2 over finite fields. For each construction, a necessary and sufficient condition for the q-ary m-th residue code and the corresponding counting formula are given. Furthermore, a criterion for that these codes are self-orthogonal or complementary dual is obtained, respectively. In some cases, a lower bound of the minimal distance for these codes is obtained.

Key words

higher residue / residue code / cyclic code / minimal distance / permutation equivalence

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Yuan Bo LIU, Qun Ying LIAO. m-th Residue Codes with Length the Product of Two Odd Primes over Finite Fields. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 353-370 https://doi.org/10.12386/A2022sxxb0028

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