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<p>Complete complementary codes (CCCs) are highly valuable in the fields of information security, radar and communication. The spectrally null constrained (SNC) problem arises in radar and modern communication systems due to the reservation or prohibition of specific spectrums from transmission. The literature on SNC-CCCs is somewhat limited in comparison to the literature on traditional CCCs. The main objective of this paper is to discover several configurations of SNC-CCCs that possess more flexibility in their parameters. The proposed construction utilises the existing CCCs and mutually orthogonal sequences and covers all lengths with the smallest alphabets <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{-1,0,1\}\)</EquationSource> </InlineEquation>. Further, SNC-CCC is extended to multiple SNC-CCCs with an inter-set zero cross-correlation zone (ZCCZ). We could control the cross-correlation magnitude outside the ZCCZ, through the proposed construction. Consequently, the resulting codes possess both aperiodic and periodic inter-set ZCCZ and feature a low magnitude of cross-correlation value outside the ZCCZ.</p>

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Multiple spectrally null constrained complete complementary codes of various lengths over small alphabet

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Rajen Kumar,
  • Palash Sarkar,
  • Prashant Kumar Srivastava,
  • Sudhan Majhi

摘要

Complete complementary codes (CCCs) are highly valuable in the fields of information security, radar and communication. The spectrally null constrained (SNC) problem arises in radar and modern communication systems due to the reservation or prohibition of specific spectrums from transmission. The literature on SNC-CCCs is somewhat limited in comparison to the literature on traditional CCCs. The main objective of this paper is to discover several configurations of SNC-CCCs that possess more flexibility in their parameters. The proposed construction utilises the existing CCCs and mutually orthogonal sequences and covers all lengths with the smallest alphabets \(\{-1,0,1\}\) . Further, SNC-CCC is extended to multiple SNC-CCCs with an inter-set zero cross-correlation zone (ZCCZ). We could control the cross-correlation magnitude outside the ZCCZ, through the proposed construction. Consequently, the resulting codes possess both aperiodic and periodic inter-set ZCCZ and feature a low magnitude of cross-correlation value outside the ZCCZ.