Chain of finite rings and construction of BCH Codes

Antonio Aparecido de Andrade, Tariq Shah, Attiq Qamar

DOI: 10.14209/sbrt.2012.3

Evento: XXX Simpósio Brasileiro de Telecomunicações (SBrT2012)

Keywords: Units of local ring BCH code McCoy rank direct product of local rings

Abstract

For a non negative integer t, let A0 ⊂ A1 ⊂ · · · ⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of suitable Galois rings with multiplicative group A ∗ i of units, and K0 ⊂ K1 ⊂ · · · ⊂ Kt−1 ⊂ Kt be the corresponding chain of unitary commutative rings, where each Ki is constructed by the direct product of corresponding residue fields of given Galois rings, with multiplicative groups K ∗ i of units. This correspondence presents four different type of construction techniques of generator polynomials of sequences of BCH codes having entries from A ∗ i and K ∗ i for each i, where 0 ≤ i ≤ t. The BCH codes constructed in [1] are limited to given code rate and error correction capability, however, proposed work offers a choice for picking a suitable BCH code concerning code rate and error correction capability.

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