Product Construction of Affine Codes
Yeow Meng Chee, Han Mao Kiah, Punarbasu Purkayastha, Patrick Sol\'e
TL;DR
This paper introduces a systematic method for constructing binary matrix codes with restricted row and column weights using products of affine codes, including a generalization to irregular products with different code rates.
Contribution
The paper presents a novel systematic construction of binary matrix codes as products of affine codes, extending to irregular products with varying code rates.
Findings
Constructed systematic binary matrix codes with restricted weights.
Generalized to irregular products of affine codes with different rates.
Applicable to power line communication for improved coded modulation.
Abstract
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of binary linear codes. Additionally, the constructions have the property that they are systematic. Subsequently, we generalize our construction to irregular product of affine codes, where the component codes are affine codes of different rates.
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